How do you level an atypical Follower?

In my last game (and also my first game as a DM), one of my players earned the loyalty of a Giant Goat (MM pg 326) by freeing it from its cell, avenging the death of its brothers by slaying a bridge troll, and reviving it back to life after it had been knocked out.

I’m not sure how I want to handle leveling from here on out. At first I considered using the Animal Companion system as a framework, but this goat is sentient and has its own bonds, so instead I’ve decided that using the Follower system as a base will be more relevant. However, the Follower system, as I understand it, assumes the follower is simply a low-level PC class. Because this follower is a beast and does not have a class, I’m not entirely sure how I should level up the goat throughout the campaign.

My initial idea is use the normal experience chart, starting at second level (chosen primarily/arbitrarily based on its HP of 19, it just seems like an appropriate starting point). It will share encounter experience with the party. If it levels, it will gain more HP using a d10 hit die plus its CON. It will also gain proficiency bonus at the appropriate levels. I don’t think I will allow stat increases, and certainly not PHB feats.

Besides HP and proficiency, the only ways to increase the goat’s efficacy will be through gear, which will require the player character to spend a lot of resources to commission an expert blacksmith to (1) study goat anatomy (2) build something that a goat could use. I also reserve the right to create a "class" feature if the story has earned it.

Those are my ideas. How do I keep the goat from being too strong but still rewarding the player character’s investment?