Not all of them. The Trailswest Campster
(shown) and Hunter Compact Jr. are good candidates, but the Hunter Compact I and Compact II are larger, heavier trailers that won't make the 1500 pound cut (and they're wider, so more wind drag).
With any vintage trailer, you have to consider how any modifications may have affected the weight. Cabinets built like those at home, for example, can get very heavy.
It's not all-molded, but another trailer to consider is a vintage Eriba Puck (rare) or a modern knock-off, the Meerkat. Dry weight starts at about 900 pounds. They have a molded fiberglass roof (with pop top) but aluminum framing and skin on the walls.
You'll need 7-pin trailer wiring and a brake controller on the vehicle and brakes
on the trailer. Many trailers this size don't have them. Finally, you'll probably want to install an auxiliary transmission fluid cooler.
In the end, it may actually be cheaper to upgrade to a tow-ready vehicle, and you'd have more trailer options.