So right now we have 2 dogs, the bloodhound and the labrador. Most of us have been wanting a pointer breed to help with pointing small game like quail, pheasant, foxes, bobcats, etc. I also think that more variety in the breeds would be nice to have as a customization for the players but also add some new mechanics. While i don't forsee this happening in the future(although maybe with enough likes we may have a shot) it's an idea I threw out on reddit a while back. Some examples would be like
Coonhounds:They add a walker, a bluetick, redbone, plott (personally my favorite), or even all, i think they'd be a great addition as a companion. This could add a new mechanic to some of the maps where they will find the scent of a animal, lets say a raccoon, and they'll chase it baying them up in a tree giving you a shot. They could do this with black bears which I think would be fun especially on multiplayer, chase deer so you or your friends can get a shot. And they'd have a new leveling system which allows you to choose what they chase, if you want them going for coons then you have to level them on a raccoon tree, so on so forth, and if you want them to just do the same thing as a bloodhound theres that option aswell in the dog circle button (have no idea what it's called but on console you hold down on the dpad to make the dog sit and stuff).
Beagles: Essentially the same as the bloodhound but in a smaller package, and I saw a post talking about burrows for animals like foxes and such, i think beagles would be great with chasing a rabbit out of a burrow or a fox. It also having a multiple level tree too choose between rabbits, foxes and bobcats.
Pittbulls: Catch dogs would be great for hogs, if your friend had a bluetick the hound could find the hog and you send your catch dog to it.
Pointers/Spaniels: These would be great for finding small birds and pointing and flushing them out. They'd have the basic system like bloodhounds and labs.