Any kind of breakup like this, even though you were probably expecting it is stressful.
From my perspective it seems like keeping the dog may hinder your ex-girlfriend from accepting new and challenging opportunities that may be available for her.
I've known two couples that broke up and then had to decide who gets custody of the dog. With one couple, the lady kept the dog, she had the more flexible job and family support. The other couple, the one with the more stable and better paying job kept the dog, that was the girlfriend. She works at our college and has the summer off and all the other holidays. She was very kind and generous like you and would let her ex have the dog when he wasn't working on the weekends and then when he moved to L.A., she would let him stay at her place when he was able to travel and get away to visit the dog.