I pulled a 21ft hybrid that was just about 4000 lbs on the road with a short wheel based 4Runner. I had an Equalizer hitch and it really helped with the stability. I had very little payload left over when the family got in so we packed lightly. Drove in some large winds and never experienced any dangerous sway. Wheelbase is an issue but not nearly as big as power and payload.
The set up was fine but I did have a bit larger engine. I would think that you could do this but the smaller engine would be a challenge in headwinds and hills. Since you should get a WD hitch even after you get your pickup truck, why not get the hitch now and use in on your Jeep? If you do feel uncomfortable then get the truck. If you feel OK then you can wait a bit like you had planned.
Is it perfect? NO Is it the best way to go? NO But, can you do it? I say yes but just remember your limitations.