Steve, there are two routes, the quicker one is through the mountains, it's very scenic and you will not have a problem in October, I would guess most of us have done this route the other way around in winter when it can be a bit dodgy with massive snow drifts, the coastal route you plan is quite a bit further and very twisty, but scenery is to die for. You will pass by Pratra, Kalkan & Kas which are lovely but I would suggest you break your trip for a stay in Adrassan (spelling?) it is lovely, hotels on the beach and a place that has not been found by mass tourism, in fact by minor tourism ! You can visit places like Olympos while there. Enjoy, because once you get to Antalya .............. !!