Do you get to choose a dog in Dog Island PS2 like do Wii?

You are likely thinking of the game *Nintendogs* for the Nintendo DS, not *Dog Island* for PS2.

There is no game called *Dog Island* for PS2.

In *Nintendogs*, you can indeed choose from a variety of different breeds of dogs to care for. This game is a pet simulator that allows players to interact with, train, and care for virtual dogs.

There are no games for the PS2 that are specifically dog simulators.