There is an alternate course for each course length. When you see a dog outrunning your character, run past your guide and it will display "Now follow the dog" which takes you to an alternate course. The dog will appear at the following locations for each course length.
 
COURSE - LOCATION
Short Course - Near the single house with a Mii outside.
Long Course - At the start.
Island Lap - At the start.

On the island lap, there are four alternate courses:

1. Follow the yellow dog at the start and then follow the black dog that appears.
2. Follow the above black dog, and then follow the white dog that appears.
3. Follow the brown dog that appears at the bridge.
4. Follow the above brown dog, and then follow the other brown dog that appears.