Is it practical to rent a car for Islay -> Inverness -> Edinburgh?

I'm an American, planning to spend 4 days in Islay in August, travel up to Inverness, then back down to Edinburgh before flying to London.

Is it practical for me to rent a car and drive this area on my own?

According to Google, Islay to Inverness is a 7 hour drive on A82, which means that the majority of a precious day is spent driving. But a taxi is about £700 :-O