Another option. From Arrochar. Beinn Narnain and A'Chrois
https://www.walkhighlands.co.uk/Forum/viewtopic.php?f=9&t=20006Far fewer sheep on that route than Ben Lomond if that matters for your dog. And once you are out the trees and heading for A'Chrois there will be far less people than on Ben Lomond.
The map shows the route striking straight up the hill from the carpark. This used to be the main path. The new path (dotted green line) is far better and I'd probably use it then cut over towards A'Chrois along a level track/path from the small dam at
NN280051
Though perhaps someone here has been up the old track recently and can comment.
PS A good circular route for bad weather is to take the new track. Turn right at the forestry track. Then follow it all the way round to Coire Grogan. From the end of the track, up onto Bealach A Mhaim then down the Cobbler track. Going up towards Bealach A Mhaim there is one point where there is a waist high fence with no gate or stile. So your dog would need lifted over.