Numbers. It's all in the numbers.
Your owners manual for your van should have a table that tells what the towing capacity of the van is (properly equipped with tow package). Most minivans properly equipped are in the 3,000-4,000 pound range for towing capacity.
You trailer has a GVWR (Gross Vehicle Weight Rating) which is the unloaded empty weight of the trailer plus the cargo carrying capacity (UVW+CCC). The GVWR is the most your camper can weigh with all the "stuff" in/on it. The trailer axle is usually the limiting factor.
It will come down to how close the GVWR is to the tow capacity. You would like to have more tow capacity than the GVWR. The issue is not getting the trailer up to speed - it's controlling it when you try to stop.
I assume you have a proper brake controller installed on the tow vehicle.
You might be fine - you just need to know your numbers.
Bama Ed
PS - I pulled a heavy popup with a mini-van with tow package and the GVWR was just under the tow capacity. So I thought I was okay. After a few brake and transmission repairs on the van, we got a bigger tow vechicle. Just sayin'.