You can use this calculator
to play with a variety of assumptions that will be particular to you and your family and how you camp. In your case, how many people are in your family and how they pack will make a difference (as shown below). So, here's my take on it...
Towing cap (GOOD): You didn't list it, but Edmunds shows the towing cap for a 2007 2500 Suburban LT with 4WD at 9,700lbs. Your trailer will weigh much more than the dry weight and hopefully less than the GVWR. Assume it comes out of the factory at 6,700lbs due to options and that you add another 1,000lbs of cargo, water, batteries, etc, than your's might weight 7,700lbs ready to camp.
9,700-7,700 = 2,000lbs cushion or 20% under the truck's maximum.
Payload (Good): At an estimated 7,700lbs, the tongue weight will be 10-15% of the camper weight or 770-1,200lbs. 13% is a good middle-ground so assume a TW of 1,000lbs. Your truck has a payload cap of 2,500lbs
2,500 - 1,000 = 1,500lbs left over for people and cargo in the truck.
But, here's where you will bump into an issue. At 1,000lbs, that TW is right at your receiver's limit, which you gave as "Weight Distributing 10,000 lbs. 1000 lbs."
You will have to keep your TW under 1,000lbs through creative packing (load more into the rear of the trailer or into the truck itself) or load less so that your trailer doesn't weigh 7,700lbs.
There's more to it, but that's a start. That calculator will help, too.