Cindy,

Technically, you can arrange your items to be picked up from storage by local movers and shipped to Florida with a long distance carrier. You will need to find movers in Northern Nevada, agree on a price and sign the paperwork (by fax). You will then need to mail them the key for the storage unit and probably notify the storage facility that your items will be picked up by movers.

Still, I would strongly recommend you to have someone you know be present at the location when the items are picked up to make sure all the items are being taken good care of, are itemized and recorded in the inventory sheet.