I bought a used 2008 Lexus GX470 (4.7L V8) in 2015, and I've been towing steadily with it for work and play. It's holding up well would tow a popup easily. If you find a Toyota 4Runner with the V8 (it was optional some years), that's basically the same vehicle. Really a V6 would handle it, but if you want more power the V8 has it.
On the V6 side, another newer Oddy van would work, or a Pilot. Or a Toyota Highlander or a bunch of other SUVs and minivans. A crew cab pickup would do it, of course.
Take a look under the trailer, back behind the wheel. If the axle has a square backer plate with some holes, that's a plate where a brake kit can be mounted. If not, for maybe $500-$800 you still could replace the axle with one that has brakes. It's not impossible.
Mike G.
Liberty is meaningless where the right to utter one's thoughts and opinions has ceased to exist. That, of all rights, is the dread of tyrants. --Frederick Douglass
photo: Yosemite Valley view from Taft Point