Hello Ozzieboy - Welcome to the Forums! All Airstreams have electric brakes. Do you mean disk brakes? If so, that's a nice move! The answer to your tow vehicle question is in your truck's owners manual and a good understanding of what that means.
First off -- the soon to be revised Airstream website doesn't have your model's tongue weight, but their old site
says it is in the range of 750#. Aftermarket options? Did you get a spare tire? That would add additional tongue weight. Your weight distribution gear and full LP tanks add most of their small additional weights to the tongue weight. Start putting your personal gear inside the trailer and you could be at 900 pounds or more tongue weight before you know it.
There are other sources, but Airstream FAQs
has a good starting explanation of loadings. Your manual will say for sure, but Edmunds
shows a number of '02 Tundra models and gives specs -- for instance, a V8 4 door 4WD Extended Cab has a Maximum Payload (or payload capacity) of 1336#. Since 900# of this payload capacity is being used for tongue weight, that leaves very little margin for driver, passengers, truck cap, gear in the bed, etc.
Listed towing capacity and GCWR might suggest you are okay. But you should exceed no capacity numbers and maximum payload is as important as they get. Much is written here about not going higher than 80-85% of any capacity number -- and that is further than I wish to go tonight.
My take is that you can safely pull the trailer home and probably start some Fall camping trip planning -- if you keep other weights in your truck to a minimum. I faced the same issue and nearly the same payload capacity with a Nissan Titan 1/2-ton I had when I bought my '06 25' FB SE. I definitely believe you should start researching toward a heavier duty tow vehicle. 3/4-ton trucks, SUVs or passenger vans are considerations. Some higher capacity 1/2-ton models may have numbers to fit your situation (eg, GM/Chev have their HD models) -- but this will take looking closer at numbers -- something to research over the winter?
Ask away -- and I hope we can get a good assortment of suggestions.