We have a 2012 Dodge Grand Caravan with 3600lb towing capacity.
Our first trailer was a 1006 PUP. We loved it, the van barely knew it was even there.
The problem we had was space, Mom Dad and 3 kids (15, 9 and 3) need ALOT of room, so we upgraded to an Eagle 14SO ... whew! 14' Dual Axle PUP with a king bed at each end.
The 14SO has a GVWR of 3330lbs, which is still within my Tow rating.
Quite a few people and dealers will tell you "Look at the dry weight, then add the weight of your stuff ..." Personally, I look at the GVWR of the trailer, the maximum it can weigh fully loaded. As long as that number is less than my tow rating, I know for certain that I am safe towing it.
In you first post, you said that you are a single mom with 1 child. (please correct me if I'm wrong) So a smaller PUP one of the 10' or even an 8' would work nicely and you would have no problems with towing safely.
Alternatively, one of the Hybrids X17? should also work well with less setup work, and still be within your limit.
Have fun and Happy Camping!
2012 Dodge Grand Caravan with Prodigy P2 Brake Controller and AirLift air-bags
2004 Jayco Eagle 14SO Pop-Up