Okay so, I just found my Nintendo DS Lite, it doesn't have my favorite game anymore.
After 6 years or more, all I remember is:
You unlocked areas with different animals, from rainforest to a savanna level where in the end you hatched a T-rex. You had to keep predator and prey apart or they would fight and one would leave. You could also put them in a bag/inventory if it was tame. I recall that in the intro of the game you tame a giraffe and you can stick him in your bag.
I really need help T-T