It's not even 1.5 miles. Honestly with heavy traffic I would probably use the pavement and/or trails if available. Looks like there's a sidewalk/path/pavement that ends at Clampernow road, and then another trail/pavement picks back up in between Tagharine and Duncastle roads. It's 1.0 miles exactly between those points. If you don't have a bicycle conducive to riding in the grass on the edge, then hit the road and sprint the distance.

I personally can't stand 2-lane roads with heavy traffic. 2-lane roads with bike lanes, or 4-lane roads where motorists can easily pass are much less stressful. If there's a shoulder, path or sidewalk (pavement) available on a 2-lane road with heavy traffic, then I'll usually take it and be extra cautious at side roads and driveways.