That is a whole lot of trailer for that vehicle! The dry TW is 902# dry wgt is 6615# GVWR is 10,000# and at 32' that thing is not going to be fun to tow. Can it be done? As long as you stay under you TV ratings yes, but that is going to be next to impossible to do. By time you load the trailer up for a week long trip you will be near that 10,000# mark and well over you SUV's tow rating.
Get a bigger tow vehicle or a smaller trailer, sorry my vote NO.
Don
Note, maybe adding E rated tires and packing lite you would be OK, but you are still asking a lot from a truck that is 12 years old!