Hello. My husband is currently in the Marines, but is getting ready to retire next month, as 20 yrs is long enough.
Since I really haven't had to move anywhere but here and we live on base, moving hasn't been an issue for me.
I do know that single people have to live in the barracks, and pets are not allowed there, so I would try to get off base housing if you can. I know here there are lots of people living off base, and there are many places that accept pets, but very few that take dogs of any size. They are there, you just have to search for them and be willing to possibly commute quite aways.
Other than the last couple of years, the military has treated my husband well, even if he is enlisted and not an officer.
It is a great opportunity and the best job security out there. Good luck with your decision. If you do join, I'm sure something can be worked out so your fur family can go with you.