Hmmm, not been "married" quarters for some time. FQ's I think you'll find, as in "families".
It's not unheard of to get one when not married, but difficult. You'll find that the entitlement is normally married or in a civil partnership. You could claim that you are the individual with caring responsiblity for your child, but that would then preclude your partner from living there too....of course who's to say if she has come to "visit".
That said, you'll save a fortune by moving into quarters...if you've the commitment to have a baby, why not the commitment to visit the Registry Office and do a quick civil ceremony, you could alway do it properly later.
What stilts said. If you were a single parent then you would be entitled to a quarter (now called Service Families Accomodation for this and other reasons...), but you're not a single parent, or even a parent just yet. If you want a quarter, get bloody married like the rest of us.