OK well yes a similar thing happened to me. It took 12 mths TTC Mason and we fell PG with Angus first go without a condom and I tested +ve the day after Masons first birthday. I never expected to conceive first go and I was happy, excited and totally horrorfied at the same time.
I had plenty of how am I going to cope moments but I managed just fine. TBH for me it was easier with a 21 month age gap than a 3 year age gap which I have between Angus and Caleb. Mason was quite content to play with his trains or just mess about while I was with Angus. I would also read him a story while I b/f if he wanted it. Two in nappies also wasn't that big of a deal either. At least you won't have to worry about toilet training regression!

Hopefully Nina will be having day naps still when bub comes along so that gives you either nice one on one bonding time with bub or if you can get bub to sleep at the same time go off and have a nap yourself.

I can only imagine how hard it would be having your partner going away with the army.
Do you have a group of friends or wives of other soldiers that could help you while he's away? I know that the guys stick together and assume it's the same for their partners as well. My brother is ex army and is still close with a big group that are like a second family to him.