I think that you will find a problem with the weight. My '64 Overlander has an empty weight of 4,700 pounds and a fully loaded weight of just about 6,000 pounds (varies between 5,775 and 6,095 depending upon length of trip). My tow vehicle immediately preceding the '99 Suburban K2500 was a '95 Chevrolet K1500/Z71 with the full trailering package and a trailer tow limit of 6,800 pounds (5.7 Liter/3.73 differentials) - - it was not a pleasant towing experience with my Overlander - - couldn't maintain 55 MPH on the gradual grade on Interstate 57 between Goreville, IL and Lick Creek, IL. The fuel mileage while towing was also terrible in comparison to the Suburban - - 9 MPG with the Z71 and 12 MPG with the Suburban (7.4 Liter/4.10 differentials - - 10,000 pound trailer towing package).
According to the Airstream web site, the least the 1972 Sovereign
of the Road would weigh is 4,700 (dry). The thing to remember with these weights is that they DO NOT include any optional equipment nor any fluids - - propane, water, etc. As an example, my '64 Overlander is listed with a dry weight of 3,930 pounds, but the actual dry weight of my trailer is 4,700 with options (main and two window awnings, 40 pound LP tanks, air conditioning, spare tire and wheel, electric tongue jack, and International package).
See the following for the factory dry weight chart:
Airstream Factory Dry Weight Chart
I suspect that when fully loaded for a longer excursion, you will be at or as much as 10% over the trailer tow rating for your Suburban. The truck will likely survive the ordeal, but you will be risking much higher than normal maintenance expense - - on my K1500/Z71 pickup, my maintenance was typically 20% to 30% higher than it is with the Suburban. I only kept the K1500 piclup for 2.5 years and 48,000 miles, my K2500 Suburban is going into its fourth year and is at 96,000 miles - - maintenance expense for the Suburban continues to be much less than the K1500 through its 48,000 miles (both trucks were special order units purchased new).
I will admit to being super critical of my tow vehicle. While still a trailering novice, I had a seriously underpowered tow vehicle (with rating to tow my trailer) and had what could have been a serious accident when the trailer had a suspension failure [1980 Nomad 18' trailer/1982 Pontiac Bonneville]. Today, if I feel that my tow vehicle is in any way underpowered or overwhelmed by the load I get very nervous. My general rule of thumb is to stay at least (and preferrably more than) 20% below my tow vehicle's maximum trailering weight rating. I also like to have enough power in my tow vehicle that I don't have to use the truck lanes when traveling - - many of the truck lanes on highways near me are downright dangerous - - cobblestone rough, with excessively uneven pavement - - the only trucks that routinely use them are the ones that don't have enough power to maintain highway speed and it seems the number is dwindling.
I hope that you have a better experience with your K1500 series Suburban than I did with my K1500 series pickup when used as a tow vehicle. The suspension was never an issue with mine - - it was horsepower and stamina of the power train.