An auxiliary transmission oil cooler might be a good investment. If you haven't already I'd recommend reading the entire towing section of your owner's manual carefully. The manufacturer may require certain optional equipment to obtain the specified 3500 pound capacity.
Since you mentioned a bathroom at one point, my personal opinion is that putting a bathroom in a 13' trailer takes up too much of the limited space. One person might be fine, but if I were planning to travel with more than one person and wanted a bath, I'd be looking at 16'ers. It will add about 500-700 pounds over a front bath 13'er. Either is well within your tow capacity, but you will feel the extra weight
going up long grades.
If you'd rather keep it light
, 13'ers without the front bath have a porta-potty compartment under the sofa and more space to hang out during a Rocky Mountain thunderstorm.
Regardless of which way you decide, trailer brakes
are going to be a necessity. Not all 13' trailers have them. If you find one and it doesn't, you'll want to check whether the axle
has a square brake mounting flange behind the hub. If so, brakes
are an easy add. If not, a new axle
will be required.