A pallat jack would be the deal, but if you can't go that route, you can pick up 4 furniture dollys from Home Depot or Harbor Freight . Lift the pallet using a 2X6 through the pallet and lift w/a floor jack to place the dollys. Keep the jack right up to the pallet, not out on the end of the board.
You might not be able to return the dollys, but you may be able to resell them if you have no other need for them.
Another idea is to mount some HD casters at the four corners and use the pallet itself as the base. Same deal for raising it up as to place the dollys. A long bit will be needed to drill the mounting holes.
Or mount the casters to a pair of 2X6 the same width as the pallet and slide the assemblies under each end and secure.