My apologies- I meant to reply to this shortly after posted, but got busy and forgot. (CRS)
I had a popup or tent camper a little while back, it weighed 3500 lbs according to the mfg label. Mine was an older model, was not configured correctly, the axle was too near to the tongue, so it had little or no tongue weight, pulled horribly. The newer ones have the axle further back and should pull better.
However, Id venture to guess that it would be the upper capacity of your 1.25" receiver hitch. Weighing your trailer is a good idea, make sure you get everything you are going to take in there, camping stuff can add considerable weight. A solid shank, very high quality ball mount would probably do it OK, but a lower quality one may pose a risk. Your trailer probably does not have brakes if it only has a 4 flat connector, so no controller is needed. Just allow for extra braking time, that heavy trailer can push you quite a bit.
Ideally a 2" aftermarket or factory hitch should be installed though.
My 302 V8 pulled my popup well, though the 4.6 is apples to oranges, but I'd say you are in good shape.