Each base has it's own policy. Most Q's don't allow pets, but it's ok for base housing. I have 2 blue-heelers and I had them with us at Quantico base housing, and now we have them at Corpus Christi base housing. We had to register them with the base and give them a copy of the shot record(s).
While we're on the topic: Blue Heelers are Australian cattle dogs (there are also Red Heelers), they are born to raise cattle, but when I was ranch working, I always took one of mine, and since I always called coyotes (daytime) I took Minni and she would sit there silently while I blew the call. I was always nervous about Mtn lions sneaking up behind me since we had a over-population of them. The year before that, 2 hunters on the same ranch were doing the same thing and a lion sneaked up within 15 yards behind them, in the day, and one guy just happened to turn around and shot it. Who knows if that thing woulda pounced on them or not. So I figured Minni's chances of hearing, smelling, or seeing a lion would be better than mine.