Welcome aboard!
A few thoughts... Keep in mind that the max towing capacity isn't the whole story - the tongue weight will be the bugaboo. Check your tongue weight (on the hitch assembly). I've seen units rated for 3500# but only a max tongue load of 350#.
The Quest has the power to do it, that's not the issue - but my concern would be for other areas, such as your tires (I'd go with a higher load-rated tire to avoid destroying them prematurely). Remember, when one end of the car goes down, the other goes up - this changes camber on both ends, which will lead to way more wear on both F and R tires. Not uncommon to see severe feathering on front tires within a few thousand miles of towing.
That trailer is at the max weight if you put ANYTHING in it. This means water, food, supplies, clothes, etc - and it adds up fast. You've got a max capacity of 3500#, and unless you plan on emptying the trailer completely, you're going to be exceeding the max.
At a minimum, I'd want to make sure you have a brake controller, a trans cooler, some sort of leveling kit (air bags), and even a sway controller. You'll want to make sure the hitch isn't super-low, or you're going to be dragging when you enter/exit driveways.
By the time you outfit it completely, you've spent a lot - and still have a rig that's going to be a rolling roadblock... The Quest isn't light - With a curb weight of 4,371 to 4,568 lbs empty, you're potentially looking at an 8k# rig going down the road.
As much as I want to encourage you to go for it, this just smells like a bad idea.
