Simple answer: yes, you must file a VA return.
That said, some things about your post are not clear. You say you are active duty military, stationed in NC but you don't say what your SLR (state of legal residence) is.
The $23,900 refers to ALL your income, not just your VA source income. The $23,900 includes you military pay, net rental profit (not total rent) and any other income, including your spouse's income. Virginia first calculates your Virginia income (VAGI) "as if" you were a VA resident. Then it prorates the income based on your VA source income and calculates the tax on the prorated amount.
If you have a net profit, on the rental, of any amount, you usually must file a VA return.
Your SLR will also tax that rental income, but will give you a credit (or partial credit) for the tax you paid to VA.
