Secure the trunk of the palm before starting to remove the plant. For smaller, younger trees, having someone hold the tree will help. For larger trees, commercial machinery may be needed to hold the tree in place. If this is the case, it may be advisable to hire professionals.
Dig around the palm carefully while the trunk is held in place. The Queen palm's root ball usually extends up to a foot from the base of the trunk, so dig at least that far away. Careful digging will allow you to avoid damaging the roots. It you encounter thick roots while digging, move a little farther from the trunk. Dig down deep enough to get below the root system and be careful to not damage the root ball if at all possible.
Pull the palm and root ball out of the hole and place it upright on a sheet of burlap. Water the root ball slightly and wrap the burlap around the roots and tie it off around the trunk. Wrapping in burlap is especially important for sandy soils to keep the roots together. Root balls with denser soils may not need to be wrapped up.
Water the root ball regularly if the palm is not going to be re-planted immediately.