For your 01 Dealers license, it could be a problem- you must have a licensed "Premises" and hours of operation- and the license is only good for that premises. To change premises, you will need to go thru another licensing inspection, show that you have business license for THAT state, comply with zoning in THAT location, have secure storage in THAT location, etc.
An 03 C&R may be a bit simpler, although prior to moving, you need to notify ATF licensing branch of your new address. Bear in mind that a C&R is NOT a license to "engage in the business" of dealing in any firearms. Says that right on the bottom of mine. It is to aid an individual collector in enhancing their collection.