As of the 2012 tax year, if you're married and under age 65 then you should file if you and your spouse earned over $19,500--and that includes his income as well. So if your spouse is in the Army then yes, you will have to pay taxes on your babysitting income.
If you're single, then your minimum goes down to $9,750.
Doesn't matter if he is not in the army you are still suppose to be certified to do child care in your home. If its for more hrs a month than what i posted above. I'm not sure where you could go off post to get certified.