Pets must be Unique to count so multiples of same pet do not count in that way but there is also a Cap of how many your Journal can hold which is 650. I made the mistake of often spending much time collecting 3 rares of many pets as I leveled only later to fill my Journal since it counts account wide all your toons pets it can fill up fast. You can crate and sell multiples of holiday pets and such that toons collected but not wild caught pets you must release them, and it hurts releasing Rares you spent so much time collecting
. You can always go back later and get multiples or better breeds of the ones useful in battles.