Public transport in/out of the mountains begins to shut down in mid September, so make sure you pay attention to schedules. Checkout: www.resrobot.se/ or http://www.ltnbd.se/ for bus and train travel info.
It will probably begin to snow by mid Sept, be be prepared for minus temperatures, especially if camping.
If not snowing, it will likely be raining.
If you head into Sarek, be prepared for some river crossings.
If you take a route requiring some boat crossings of lakes, be aware that some of the boats are pulled towards the end of Sept, so make sure not to get stuck between two lakes.
Most of the huts close around the 20th of Sept. But they usually have an emergency room that is left open that one can use. If you head into Norway, you will need a DNT hut key.