Played it on a friend's device, it is a cute game and a nice time killer. Kind of surprised Nintendo hasn't done more with the series.
The cartridge will be fine and the original save file will be on it which would be good for you to see! That virtual pet needs you...I loved Nintendogs! I believe we still have the game in storage somewhere as my daughter kept her copy of the game and I know we still have a Nintendo DS in storage too.
It would be awesome to go back to the game at some point, not sure if the game we have would still work.