We pulled that size popup with a 2010 Pilot and it worked pretty well. That's not what I'd go out and buy for towing, though, we just happened to have one.
I would recommend a half ton truck at least. Yes it's more than you need for that trailer, but the general progression is that you will more than likely upgrade to a larger trailer in the future and getting a more capable tow vehicle now will help make that an easier process. Plus you have two little kids. Little kids like to have stuff with them, and they don't stay little for very long. Having extra capacity and cargo space is a lot better than being tight on either. I think you would appreciate having a truck bed for kid toys, bikes, dog kennel, extra water, chainsaw, BBQ, etc., etc. Popups are pretty limited in the cargo carrying department.