THe QX80 has an 8500 pound tow rating with AWD. 7500 pounds dry is 8500-9000 pounds loaded with 1000-1200 pounds of tongue weight. That's beyond the capability of any half ton SUV and even the very rare payload improving packages of half ton pickups. There are no SUVs after 2007 that can handle more than 1000 pounds of tongue weight. Half ton SUVS tend to have 1200-1600 pounds of payload, which needs to support the dog, your baby and child seat, wife, you, and any other cargo in the vehicle. As you test drive vehicles, look for this sticker when you open the driver's listing as equipped payload. Note what is listed where mine says 2051. You'll want at least 1500 pounds. My research from shopping more heavily optioned SUVs 3 years ago was half tons won't cut it for towing and hauling a family.
You also want to check the recevier ratings. They are typically limited when using a WDH to 10% of tow rating. The GM SUVs at 1000 pounds are the highest, despite the tow rating the lowest. But for RVs with 12-15% loaded tongue weights, that's often the limit much lower than the 8000+ tow rating. 850 pounds of TW at 15% is only 5667 pound trailer, or 12% TW 7100 pounds. 1000 pound limit would be 6667 pounds at 15% tongue weight and 8333 at 12%.
Are you willing to put the dog in the bed of a pickup with a enclosed cap? Pickups cost about $8k less for the same equipment as an SUV and offer a lot more cargo capability and uses. Bed covers range from $200-2000. You pay a lot of money for that climate controlled cargo space and 3rd row. The second row of seats are typically larger than SUVs as well. Receivers are also rated a little higher at 1100-1250 pounds.
Besides that, a 37' TT triple bunkhouse is excessive for a family with one infant child. Your child will be sleeping in a pack and play for 2 years. 37' will limit the number and types of campsites as well.
You may wish to reconsider your thoughts on American SUVs. Check out a quote from
this article about the 2015 Ford Expy.
I can't over-emphasize how much more popular the GM SUVs are. Last year 38,350 Expeditions were sold compared to 51,260 Suburbans, 83,502 Tahoes, 28,302 GMC Yukons, and 31,258 Yukon XLs. (That's 194,322 SUVs out of The General's showrooms). A few people bought Land Cruisers and Armadas too, but I don't think GM's product planners have heard of those vehicles.
Toyota sells about 15k Sequoias. The GM or Ford SUVs may not be the best for everything, but clearly they are the best compromise for most of the market and there are valid reasons for that. I love my 2011 Suburban 2500. But I know it isn't the best at everything. Right now, I would strongly consider the 2015 Expy with Ecoboost if it had enough payload for towing.