The cheapest option with auto-tracking is going to be the Dahua
SD49225XA-HNR IF you buy it from Loryta/Empire Andy on the forum or his
Amazon Store. Dahua has updated the hardware on that model and only the older models with a specific Loryta firmware version will still have the autotracking. I believe Andy still has some stock available, but he will eventually run out of these older hardware versions. It runs about $400 from Andy. It's only a 2mp camera, but don't let that fool you. It has a pretty small sensor size, so the fact that it is only 2mp allows it to perform very well at night. The limited resolution is also offset by the fact that you can zoom in with the PTZ. There is also a SD494225 PTZ camera available, but it is a 4mp camera with the same size sensor as the SD49225, so the low light performance isn't going to be as good.
The only negative comment that people make about the 49225 model is that the auto-tracking will immediately loose it's subject if it stops moving or passes behind a tree or other structure (which is the same thing as "stops moving" to the camera's AI algorithms). The AI isn't quite good enough to predict the subject will continue past an object and pick it up once it becomes visible again. Instead it simply resets back to it's set "PTZ location" and resets it's event detection. It will also only track a subject for up to a maximum of between 15 and 300 seconds as defined in the cameras settings. So the camera will never simply "follow" your dog around all day. If set for the max 300 seconds, the camera will follow until the dog stops moving or 300 seconds - which ever is shorter, then reset to it's programmed PTZ position, then detect when something starts moving and start following it for another 300 seconds, etc, etc, etc.
I cannot remember the model number of the next cheapest (decent) PTZ camera you will want to look at (maybe the SD5A425XA-HNR), but it's about twice as expensive. These more expensive options can have better AI predictive tracking, larger sensors and more resolution, so they can be attractive if you have the budget. Personally if my main goal was watching my dog, I'd stick with the SD49225 for the best feature/cost benefit.