A9 - about 1 1/2 hours. Is this a nice scenic ride? It looks to be mostly “highway.”
I see you have also posted this on Trip Advisor, and you haven't responded to the very good answer of adding in stops at Pitlochry and Dunkeld. House of Bruar (the 'Harrods of the North' is more debatable but there is a very nice short scenic walk you can do from their parking lot).
That is a wildly optimistic timing. It is highway, and if you go onto the M90 at Perth is 2 hours 3 minutes according to AA route planners. Stay on the A9 into Edinburgh and it adds another 30 minutes. I really would not like to see anyone trying to do that journey in your timing. Not saying it's impossible (we do have several drivers like that on this forum) but it is aggressive driving and (if not actually stopped by a traffic policeman) you'll be getting speeding tickets in the mail afterwards. I don't want to be on the same road as you.
Scenic Option - about 2 hrs 15 min - General Wade’s Military Road along the Tay National Park to the B846 and crossing the River Tummel then turning to drive along the River Lyon and then the A827 along the north side of Loch Tay to the A85 then the A84 to Doune.
I would go further and say that is a lot more scenic, and you see a lot more of the country but wonder what the huge rush is. That route takes you past the Scottish Crannog Centre, which is a highly recommended stop over. And I would even suggest a short divert into Aberfeldy as well.
It is all but 90 minutes from Dalwhinnie to Killin- the A85 junction, then 50 minutes on to Doune Castle, then a further 75 minutes on to Edinburgh- so that is about 3 hours 30 minutes at least without significant stops.
Coming off the A84 just west of Callander you could even add a diversion into the Trossachs proper and down through Aberfoyle then the A873 straight into Stirling. This route could (and should?) be a full day's trip