Besides tow rating, you have a few other ratings to consider. Your receiver is rated at about 950 pounds. That's about a 7500 pound loaded TT, but maybe as low as 6500. Payload for the tow vehicle may also be a limit. It needs to be enough for the TW and everything you plan to put in the SUV. People, games, stuff to occupy their time while traveling. So with your listed estimates and 950 pounds of TW, 1200 pounds is not enough and 1500 pounds of payload is. Look at that Tire and Loading sticker on your driver's door for as equipped payload.
Practically, I agree that you will want to stay near 6000 pounds dry. Length does not matter, focus on weight. When you add clothes, food, chairs, grill, cooking and eating stuff, toys, etc, expect about 1000 pounds over any RV listed dry weight. More if you plan to carry full fresh water tank. Also, the % of half ton owners towing 7000+ pound RVs that are satisfied is fairly low and about 50% upgrade to something more capable. Meanwhile, under 6k people are reasonably pleased.
Get a proportional brake controller and WDH with integrated sway control.