First contact the VA AG for a ruling on the law:
§ 18.2-304. Manufacturer's and dealer's register; inspection of stock.
Every manufacturer or dealer shall keep a register of all "sawed-off" shotguns and "sawed-off" rifles manufactured or handled by him. This register shall show the model and serial number, date of manufacture, sale, loan, gift, delivery or receipt of every "sawed-off" shotgun and "sawed-off" rifle, the name, address, and occupation of the person to whom the "sawed-off" shotgun or "sawed-off" rifle was sold, loaned, given or delivered, or from whom it was received. Upon demand every manufacturer or dealer shall permit any marshal, sheriff or police officer to inspect his entire stock of "sawed-off" shotguns and "sawed-off" rifles, and "sawed-off" shotgun or "sawed-off" rifle barrels, and shall produce the register, herein required, for inspection. A violation of any provision of this section shall be punishable as a Class 3 misdemeanor.
(Code 1950, § 18.1-268.6; 1968, c. 661; 1975, cc. 14, 15; 1992, c. 580.)
Second, I would guess you as a person not engaged in the business of manufacturing or dealing in firearms do not meet the definition of a "manufacturer" or "dealer".
As a dealer, I DO keep a serperate bound book on all my Title II firearms, always available for inspection. Note that I do meet the definition of the term dealer and manufacturer.