It's found in the little place where you have a timer counting and you are riding on Lapras.
You can only find Psyduck after you catch all the Sharpedo/Carvanha on the southeast side of the course.
After doing that, it should appear near the same area floating on the water.
I should warn you that psyduck takes 30 circles to obtain, which is a b*tch (thankfully, it doesn't move much). >_>