I’m seeing quite a bit of confusion in this topic so maybe we can back up a minute and look at a couple of the basic concepts and then look at a couple of the possible devices. Because it is possible to do this, it just may not work quite the way people originally expected.
Part 1: Presence in SmartThings
“Presence” in SmartThings is way simpler than most people expect. All you need is a device type Handler with “capability.presence” and then that presence can be turned on and off for that device. (Of course you have to have a reason to turn present on or off, that is an event that you can capture, but that’s a separate issue.)
This capability is why you can have a virtual presence sensor, which is just a virtual switch, and you can turn that virtual switch on and off from within SmartThings or with IFTTT or some other options. 
There are also all kinds of hardware devices that you can use as presence indicators.
If you want to use a mobile phone, you can install the SmartThings mobile app, but you don’t have to. If for any reason you don’t want to install the SmartThings mobile app, you can use the official life 360 integration. It’s quite popular.
Or you can use android presence and tasker and sharptools. Or the IFTTT presence.
Again, as long as you end up with a device type handler in SmartThings which has “capability.presence” you can turn presence on and off.
If you want to use a physical device that broadcasts an arrival event, you can use the official SmartThings brand key fob presence sensor.
But you could also use an IBeacon or any other device whose presence could be captured in such a way that you could then flip on a virtual presence indicator.
You could even have one of those pet doors that has a microchip reader installed as long as you can capture the data and then, again, use it to turn on a virtual presence sensor.
The key again is to use a virtual presence sensor which you will turn on and off because of other detectable events.
So another aspect of this is that any device which can send a text message or an email could be used to then trigger turning on the virtual presence sensor.
If you have an android phone, you can capture the message as a trigger event with Tasker.
If you have some other kind of phone, you can probably do it with IFTTT, it’s just a question if you’re going to run into message limits per month.
Also, if your original device can do webhooks or an RSS feed, you can pick it up in IFTTT that way, probably without message limits.
So if you have a GPS tracker like whistle or one of its competitors, it’s very likely that it already has a means of sending texts to your phone or emails to you as your pet passes various locations. Then you set things up so that receiving one of those texts turns your virtual presence sensor on or off. The Exact method will vary depending on the specific device you have and the phone that you have, but it’s almost always doable. 
Part 2: The Detection Zone
So now you have a device that you like which is capable of turning a virtual presence sensor on or off. Excellent. The next question is when do you want to turn it on and off. That is, what is the size and shape of your “detection zone.”
If you are using anything which is GPS-based, including the phone, then your detection zone is probably quite large. Usually the smallest is a 500 foot radius.
If you want to use a smaller zone, you have to switch to a different kind of device, typically Zigbee or Bluetooth but maybe Wi-Fi based. These have a receiving device at the center of their detection zone and then they just report on whether the device has left the zone or not.
The problem with all of these is that radio frequencies pass through walls. So these are good for things like “the dog left the house.” But typically they can’t tell the difference between one room and the next and they can’t usually tell the difference between “in the house” and “in the yard.”
It is possible to set up what is called a “microlocation” system where you can tell if the dog is in an individual room, but you almost always have to invest in a lot more devices and it gets much more expensive. As much as $300 per room.
For more discussion of microlocation approaches, see the following recent thread:
But for the purposes of this thread, let’s just say that in general if you want to identify the dog’s location the same way you would track a phone, you would use a GPS-based presence. The detection area is a pretty big area each time, but you could track the dog all over the city if you needed while only needing the one device which is attached to the dogs collar. For this you would probably use one of the GPS location collar devices like whistle. There are a number of different brands, but again most do have monthly subscription plans.
If you just want to get a notification if your dog has left your property, but you won’t necessarily know exactly where the dog is, just that she’s “Home” or “away,” then you can use a Bluetooth or Wi-Fi or zigbee based device.
If you use an IBeacon (which is Bluetooth based), you’ll have the most control over the detection zone, and can get it down to within a few feet. But there’s still that issue of signal passing through walls that you have to take into account. And you need to have a “receiving” device in every detection zone, so you can set this up at home, but it won’t tell you where your dog is if she gets out of the house.
If you really want to know if the dog is in a particular room, it’s probably doable, but it’s a much more expensive system with a lot more devices.
Many people end up just using cameras for this and checking in to see where the dog is but if you really want a system that notifies you if the dog has gone from the bedroom to the laundry room, you can do it. But see the microlocation threads for that.
Conclusion
Once you understand that in SmartThings presence is just a matter of turning on any device type handler that has capability.presence when some capturable arrival event occurs, it opens up potential solutions to all kinds of different devices and methodologies.
You need something that can announce its arrival in a particular zone. But as long as that something can send a text, an email, RSS feed, or web hook, then you can connect it to SmartThings by using a virtual presence sensor.
Or maybe it’s a different kind of device like a microchip reader where you can capture its information in some other way. Again, the same idea: use the arrival event to turn on the virtual presence sensor and you’ll have full integration with SmartThings. 
Often the trickiest part is determining what the detection zone will be. And taking into account the fact that radio signals pass through walls. Most people end up compromising with a larger detection zone because it’s just simpler and less expensive. But if you really want to go down to the room by room level and you’re willing to spend $300 or more per room, you should be able to get that to work as well.
I hope that explains how you might approach a dog collar project and what sort of factors you might have to address.
Different people will come up with different solutions both because they want different types of tracking and because they have different budgets. But there are a lot of creative things that you can do depending on exactly what you’re trying to accomplish.