From what i have seen on another shard pet breeding is very beneficial, in that shard pets had certain amounts of breedings and not all of same breed were breedable. If you breed a pet it ups thier stats, so for pet lvl 1 bred to another pet lvl 1 would produce a pet lvl 2 with higher attributes. not sure if it is the same here since we didnt have pet lvling at my last play time.

Yes that is how it works.