Five of us have just done this route (last week of this August)- the other 4 were joining me from Queensferry to JoG as the last part of a LeJog that I have done in stages.
(for the backstory see
https://hughwill69.wordpress.com/ )
As always the reality is somewhere between Mick F's 'no problems at all' and the 'it's horrible and a nightmare and the other routes are so picturesque etc.
You mention Dornoch- I presume you mean the Dornoch Bridge. From what we experienced the A9 up to this point is pretty horrible- we had used the entirely rideable (though watch out at times for potholes) cycle route from Perth, most of which is reasonable road or tarmac trails. By the way, while we passed they were resurfacing the bike path drop down from the Drumochter Pass- the surface is like a billiard table and with a following wind we averaged nearly 30mph for over a mile. Stunning!
From Dornoch Bridge (upon which we were serially close-passed) we turned off to go through Dornoch itself. Nice route adding a couple of miles but reducing the amount of ascent. Once rejoining the A9 at The Mound we used the main (and only) road all the way up to John O'Groats. In traffic terms it was O.K. Most traffic (particularly big trucks) gave us plenty of room and didn't try to overtake on blind corners of summits. But you will always get some who are ignorant, don't care or resentful on any road. This part of the A9 is not the worst and sadly I think any Lejogger has to be prepared for bad behaviour from vehicles on any roads chosen.
The road through Golspe, Brora and up to Helmsdale was uneventful. My companions in their 30s and 40s found the hill beyond Helmsdale pretty monstrous (the rain didn't help) and how I managed it I don't know. It was the hardest hill of the whole LEJoG in my experience. After this came the Berridale Braes. The steepness of this monster is well known. We went through it in driving rain with full braking on the downward slope through the surface water. As many know there are road works on the other side. The state of these were not very cycle friendly. While we could ride up on the inside of the cones for some distance we had in the end to join the single narrow lane. We never knew when the southbound traffic being held up by the lights would be released into the single narrow lane we were crawling up- it was somewhat scary since at the end we were going round a blind corner..........at least it distracted from the fact that the hill is a beast for cyclists in normal times!
The last part through Lybster, Thrumster, and Wick was fine. Not a huge amount of traffic and generally respectful apart, confusingly, from a large number of Dutch (yes, Dutch) Motorhomes which attempted to nudge us into the ditch.
Overall, I would say that unless you are very apprehensive about any traffic it's ok.