Charlie
On the assumption you are going direct (driving ?) from Prestwick to Dornoch you will be taking the A77 to Glasgow, followed by the M80 that leads on to the M9/A9 to Inverness. From there it is a relatively straight forward journey to Dornoch. On that basis you wouldn't be going by Loch Lomond but you would be going by Gleneagles and about a hundred other courses (huge generalisation on my part) and not really possible to discuss them all in one post.
Ignoring anything south of Prestwick, there are about 10 or 11 links courses a short distance to the north of Prestwick and before you get onto the A77 that vary in quality from good fun muni's to Open Championship course and most being at least an Open Qualifier. Happy to give you a full run down.
There are 30 to 40 parkland and moorland courses in and around Glasgow, many of which are worth playing including Colt, MacKenzie, Braid and Old Tom Morris courses. Nearly all are members clubs but happy to take visitors.
Beyond Glasgow there are several courses worth stopping off at on the way north including some of those already mentioned such as Blairgowrie, Gleneagles, Pitlochry and Rosemount. To that I would add Glenbervie, Grantown on Spey, Kingussie and Elgin. I'd also urge you to look out some of the funky nine holers that proliferate up that way including Strathtay, Nethy Bridge, Covesea, as well as the ones north of Inverness.
If you are going to look at Castle Stuart then suggest you come off the A9 at Aviemore and take the A95 to Lossiemouth/Elgin and from there work your way along the coast to Inverness. And while I don't seriously expect you to take my advice over Tom D, I'd question what you are really after, do you want to play the best links or a good modern design, because if its the former then (IMO) its a choice of between Royal Troon, Moray Old (Lossiemouth) and Nairn and Castle Stuart (slightly ahead of Dundonald) if its the later.
Niall