For the record: Not a PT, but a current member working in healthcare with some experience working in an active duty hospital.
I feel like working as a civilian PT on a military installation may be difficult *to get into*, considering most PTs I've ever encountered in the military were active duty PTs. When I was stationed at Wright-Patt, I saw a PT a couple of times and my appointments were always with military PT (don't think I saw a civilian PT there).
I just did a USAjobs.gov job search for physical therapists and there are multiple positions open across the country to work at Air Force installations (to my surprise). You may need to be a bit flexible as far as where you want to live/work considering there's postings in Alaska, Ohio, Utah, etc. Since you're a military veteran (thank you for your service), you'll be a preferred candidate (I would assume) given the security clearance, military status, etc.
Hopefully this information helps you. Good luck with the rest of your schooling and future job search!
*Edit: Wanted to clarify what was exactly difficult.*