Are you going from Glasgow to Edinburgh to Kennacraig, or directly to Kennacraig from Glasgow? You'll need to drive over to Kennacraig to catch the ferry to Islay. Mid to late September is not a problem for visiting Islay, although there's always the possibility of ferry cancellation if the seas are rough. The ferry departs four or five times daily. Some ferries travel to Port Ellen; others depart for Port Askaig. You may want to sail to one; depart from the other.
Total driving time from Glasgow to Kennacraig, which is south of Oban, is about 4 to 4 1/2 hours. Add an extra 1 1/2 hours from Edinburgh. Ferry services are operated by Caledonian MacBrayne (CalMac). Check their website for times and fares. As Islay has become more popular over the recent years due to the popularity of distillery touring, I'd advise making lodging reservations as soon as you've finalized your travel plans. Ferry reservations should be made at least a week ahead of time. You need to spend at least two nights on Islay.
p.s.: As you haven't yet experienced driving on the left, I'd advise picking up your hired car at Glasgow Airport as opposed to in the city. That way, you'll get a little bit of experience before driving off to Kennacraig or Edinburgh. Driving in the center of Glasgow can be very nerve-wracking, with the bike lane and bus lane cameras everywhere, and getting stuck at a traffic light at the top of a steep hill, driving a six-speed, with another car directly behind you, is an adventure in itself!