Welcome, Beth!
One thing you're up against is that showers in 13' trailers are a fairly recent development. I'm not sure when
Scamp and
Casita came out with their front bath models, but they would hardly qualify as "vintage" and probably wouldn't be exactly inexpensive either, unless they needed a lot of work.
On the other hand, adding a shower to a vintage unit, while possible, is far from a beginner's project. It means adding a hot water heater ($$), a shower pan and surround, a grey water tank, and plumbing for hot water, cold water, drain water, and
propane. And are you looking for a toilet, too?
One place to begin your research is the classified archive at
fiberglass-rv-4sale.com to get a feel for what's out there and at what price points. I'd start with recent
Scamp and
Casita sales looking for front bath 13'ers.
Best wishes in finding what will work for you!