If you look at car trailers they are always tandem axle. Yes, a good single axle costs more, but I don't think it is double. There is also a lot more work in making a tandem axle trailer, alignment of axles, spring equalizer, etc. So there are reasons tandem works better then just one big single axle or else the cheap trailer builders would simply be making single axle trailers with beefier suspension.
So a second axle is a good upgrade. But just adding a new axle in front of the existing will alter the load distribution. If the existing trailer is correctly balanced on a single axle, adding a second will require relocating the original axle to get the trailer to balance out correctly.
More thoughts, a free trailer rarely has a set of new tires on it. How old are the tires? There is a date code at the end of the DOT number. Are the existing tires even worth keeping?
At one time I almost built a single axle car trailer, out of the frame section of a motorhome. Rated tires, springs with capacity, really big brakes. In my head it would have worked. Never made it. Something just wasn't "right" about it.
My thoughts on this trailer. Sell it as a quad/ATV/utility trailer. It looks very good for that application. Get a proper car trailer. Or at least a good tandem axle boat trailer for a heavy boat (3+ton) and start again.
For reference, the scariest trailer I ever pulled was a pickup bed trailer with 1100 pounds in it. It was an empty water tank with a high CG (Bronco has a high CG sitting on a trailer) and it was a single axle trailer. Rolled, rocked, swayed, unstable, unsafe, and it was only 12 miles and took nearly an hour at 15 MPH.