I am running a game for my son and his friends. My son bought a mastiff. I am wondering if the dog should gain experience and advance in levels. I have not thought of how to do this. If the dog does not gain levels it will eventually become useless as the party becomes higher level and is fighting more powerful monsters.
If your son is not a ranger, no.
Animals, wild or domestic, have their own statblock as described in the MM or the PHB.
However you still can homebrew this:
During the downtime between two adventures, you can suggest your son train his dog, it can gain like this (only one a time):
- One hit die
- Adding your proficiency to one skill like perception, survival
But remember it should not be too overpowered (not be as powerful as a ranger's beast) and remind your son that resurrecting his dog might not be possible, or at least very expensive.