It's pretty much right at peak this weekend, so next week will be late for the max color. Next week's weather is supposed to be GREAT! Highs and lows in Gatlinburg are to be (highs and lows) 82 and 56 on Monday, 78 and 55 on Tuesday, 72 and 54 on Wednesday with a 40% chance of rain, 67 and 49 on Thursday with 50% chance of rain, and Friday is 59 and 39.
If you are in the mountains above Gatlinburg, it will be about 10 degrees cooler, but this is wonderful fall weather.
It should be a wonderful time to visit.
I would continue down I-81 until it ends, then hit I-40. Spend a day or two there are GSMNP. You can travel on down I-40W to I-75S, then to I-59S to I-65 to Pensacola. I don't know where you are heading in FL, but this will take you about 8 hours from the Gatlinburg area.