The dolly can be pushed around and will run over zombies, similar to the utility cart. To push the dolly, the dolly must initially be in an upright position. If the dolly is laying down, pick it up and then press to put the dolly in an upright position.
If the dolly is set to be a dispenser (IsDispenser = "true" in the game files, via a mod), the dolly dispenser itself can be pushed and moved to a different area.