Welcome!
I have knowingly towed close my max on 2 different combos. It's doable but not ideal. Towing with a decent margin is a far better experience.
I see two problems
1) Tongue weight. Your trailer's weight loaded for camping will more like 4000#-4500#. So you're looking at tongue weights of potentially in the range of 500-600#. That's well over your limit, not just max.
2) Payload. Check the weight sticker in the driver door for your available payload. A passenger car is going to be somewhere between 900# and 1100#. Subtract 100# for your WD hitch, subtract 500 for tongue weight. You have 500# left for your family, dog and stuff. Not a lot of room to play with here. Likely you won't be over, but you'll be very close.
If you choose to tow this trailer, you'll be putting far more strain on your car than it was designed for. If I were you I'd be looking at a large SUV like a Durango or Suburban, or 1/2 ton PU. You'll have a far better towing experience.