Just to echo what PPs have said. We do this trip several times a year.
You'll easily get to Inverness if you set off early. We set off early and stop north of Birmingham to have a huge breakfast. Our next stop is at Tebay. After that we just have a quick pee and petrol stop north of Glasgow. So,our route is M40, M42, M6 inc the toll road, M74, bypass Glasgow, M9, A9. You have the advantage of long light nights at this time of year.
Take care on the A9 though especially the northern part south of Aviemore. You need your wits about you as it isn't dual carriageway. Sections are but only a few miles at a time for overtaking.
It can be disorienting as in parts you can't actually see the other carriageway as you're in an elevated position and the other carriageway is out of sight. So you need to be on the ball and know whether it's single or dual carriageway. Lots of fatal head on collisions where drivers forget it's no longer dual carriageway. There can also be speed freaks on the road. Police regularly catch drivers doing 122/138mph..
Something else to bear in mind going to Ullapool. The tourist board have done a great job of marketing the North Coast 500 road trip. www.northcoast500.com. It's a scenic, Scottish version of Route 66, a 500 mile loop starting and ending in Inverness. There's a lot of holiday traffic on the road anyway and even more now with Nc500. You get groups of anything from campervans, motorbikes, Ferraris. I've been up west in April and looked in my rear view and thought oh that looks like a Ferrari in the distance, pulled over only for a fleet of high end fast cars go,past.
For stopping in Inverness, there's a Holiday Inn Express on the outskirts. It's a good place to stop and easy to get across the bridge from there in the morning. There's a pub just a 2 minute walk away called the Snow Goose that does good pub food.
Have you considered flying to Inverness and hiring a car? Might be worth checking out costs of both options inc a hotel stay and fuel costs.
Btw, we always come back south in one go and don't stay overnight. Reason being the roads get better the further south you go and once you get to Birmingham you might as well keep going.