I am another military wife (Go Navy!), with 3 small children. They are a bit older now and almost all in school (just one more to go) but last deployment I had both my little ones home with me. The trading with a buddy suggestion is awesome, or if you can afford it find a local gym with daycare. I actually found one last sea duty that was only $35 a month, and the daycare was available everyday but sunday. It was a lifesaver for me. If not, I agree with Kara, get some good dvds. There are also quite a few exercises out there that you can use your little one as your weights and he'll think it's great fun playing with mommy. My kids still like to make me do leg lifts with them as weights and stuff.
Good luck, and nice to see more military wives around here. We are facing our first deployment in 3 years and it's going to be a doozy, my husband will be doing an IA in Iraq for a year to 15 months.