Here's the rub - without 12 months of employment (1250 hours) immediately prior to your leave, you won't be eligible for FMLA. This is true across the board, and not just specific to the VA or federal employment. So all you will be able to take is whatever leave time you have accrued, and anything other than that won't be protected.
With 12 months under your belt, you would at least be eligible for your 12 weeks of time off - they will likely not pay you for that, but you can use your accrued leave to get paid for at least part of it and choose to take the rest unpaid.
I was not at the VA... but when I had my first child, I was able to use sick days to pay for 6 weeks of my maternity leave, and then did another 4 weeks unpaid. But because of finances, that was the most we felt comfortable doing unpaid. So I basically shaved off 2 weeks, which wasn't ideal but it wasn't horrible, either.
Anyway, pregnancy is (give or take) 40 weeks. So if you held off for just a couple of months before getting pregnant, you are likely to have your 1250 hours under your belt before delivering the baby. It may be worth it, as you will have more sick time accrued (to pay for your time off) and you will be eligible for FMLA.
There may be some VA-specific issues I'm unaware of, but that's the generic version of maternity leave (I've had two at two different institutions, and the experiences were pretty much the same at both).
ETA: Also, if you are doing your internship at a different VA, it might be that those hours would count toward your "12 months" as you are remaining within the VA system? But that might be a stretch.