PA12DRIVER has it right - things will be closing up very shortly after the Labor Day weekend. If you like to stay in RV parks most of them will be closed early in the month. However, having said that, if you rent a unit with a generator, Alaska has a lot more places to just camp on your own than other states if you watch your tanks and propane for heat. The gas stations will be open.
And as he said, snow will/could be a problem. I live in Anchorage now days but always head north to go moose hunting. Going up isn't a problem, but coming back south we usually have snow. Sometimes it only lasts a day or two and other times it lasts for the winter. The main problem is wherever you go, you're going to have to travel the higher passes to get there. So while the main places like Anch, Kenai, Seward, Valdez, Fairbanks and so on are mostly at lower elevations, you're going to have to travel the higher elevations to get between them.
I'd plan on being back in the Anch area by the second week in Sept unless your schedule is very flexible. These were taken on Sept 25th.

Note the chains on the tractor - I spun out on one of the hills.

Bill