As it is now a lot of the smaller nice details kind of get lost and some of the pets are just kind of hard to visually read in general with just their small icon in the equipment slot.
I propose giving them a tab all for themselves and just make it basically a scrolling gallery with all the pets you have collected to choose from. This would allow you to get a much better full size look of them and appreciate all their smaller details and even in the future open up the possibility of some pet training related stuff down the line where they can earn xp of their own and level up or something like that.