I don't know about the specifics of American base housing. As a civilian, perhaps he can negotiate off-base housing as part of his contract? If so, it gives you some options. Keep in mind that he won't have transportation until he has residency which can take 4-6 weeks after arrival. The way around this is (maybe) is to arrive with an International Driving Permit and pay for a temporary driver's licence upon arrival.

Identifying yourself as a cohabitating girlfriend/boyfriend is a definite no-no. Either come with a government issued marriage certificate before you arrive, or find your own employment contract. Don't get me wrong, cohabitating is done here but not officially and you can probably only get away with it if you are non-Muslim and Caucasian and keep it very discrete (assisted by living in a Western ex-pat villa/apartment).

Unless you're married, he can't sponsor you as a dependent. Without sponsorship or your own employment contract, you can only come on a 2 (or 3) week visitors visa--renewable only once--before you have to leave and come back again. Fines for overstaying a visitor's visa are 50QR/day.

My wife is much in the same employment situation. She's a social worker. There isn't really much of a social work/secular mental health industry here. You might be able to hang out a shingle once you get here and do counselling for EAP programs with ex-pat employers or private counselling for ex-pats and their families (Lord knows there is a need here), but private counselling won't qualify for an entry visa either.

If he's serious about coming and your relationship is solid, then get married (or sign a pre-nup and get married). The housing still needs to be worked out (as per scmasse), but you can have a very nice honeymoon for the next few years. It really is an amazing country once you get past the marital conservatism of Islam.