I agree that's too much trailer. That's a very large trailer and a short wheelbase tow vehicle. With the hitch weight, you'll easily be overloaded on payload. I have no doubts the Infiniti "could" pull it, it just wouldn't be comfortable, and possibly unsafe.
If you have a bias against American vehicles (understood, they made terrible cars for years) you may want to take a second look at the new generation of American large SUV's. The new Escalade/tahoe/suburban/Yukon is an excellent vehicle. The same can be said for the aging, but recently refreshed, Expedition with Ecoboost power.
I owned an Infiniti before my truck (2007 G35X), had no complaints. I was in the same boat as you with a certain bias towards foreign. The recent advances of American manufacturers is impressive.
One of the reasons I bought my TT was for when an infant comes into the picture for our family. There is a separate front bunk room that would be a great kids room. Not many windows to keep light down, and away from the noise.