To the OP:
As others have noted in this thread, one of the main hurdles about taking care of a pet while in grad school will involve your housing situation.
If you are enrolled in grad school, you will likely be renting (often with roommates), either in housing provided by the university, or in off-campus housing (e.g. rented house, apartment, condos, etc.). And different housing may have different rules in terms of allowing pets. I know many landlords have a strict "no pet" rule, which may preclude having your dog with you.