Hello,
A mounting system is great for the end game. When we're in leveling time, is excellent to walk slow and see the beautiful world we have to explore. But at a high level, perhaps we can return just to do another quest and it's helpful to walk fast.
The idea that we find the pet and take care of it till the time we can mount is cool. Tame, feed, and make it happy is a nice way to create a link with our mount. And it should be at the beginning of the adventure because notices the pet is growing too fast is strange.
But it needs to do one way we don't be locked in the system with fear of the pet die or don't be good enough. This system may look like a mobile game and may don't be good.
I don't like the idea of habilities for mounts, it can unbalance making everyone use one particular mount just for the bonus. Fly mount is another thing that can lose the ambient immersion feeling.
I know that even the things I don't like if made with care will be amazing.
Great job.