Most dreams in humans occur during REM sleep where the muscles are temporary paralysed so there will be no movement also sleep talking comes when we are coming out of REM sleep.

We can only assume that in dogs the movements and whimpering does not occur in the REM dream state.
Ref: "Wag,The Science of Making your Dog Happy" by Zazie Todd.

I would like to think my dogs dream of fun stuff whether they are moving or not.