Or if she's named after a theme, the "Starship" theme, then the theme spanned 10xx for the Constellation to 17xx for the Enterprise. It would be possible for the Enterprise to be the 1st ship of the 17th batch or series - although the question then is should not the first ship of that batch be NCC-1700?
:XX00 = Prototype/Testbed for XXth series of Starship (Often placed into service after testing is complete); XX01 = First production model.
Also, Starship could be a very broad classification, though one it was felt was signifigant enough to use on the dedication plaque (since in the 2260s there seems to have been a big difference between Space Ships and Star Ships). Maybe something like:
- Starship Class
- Heavy Cruiser Class
- Light Cruiser Class
- Spaceship Class
Later the term "starship" became more and more used colloquially to refer to any Starfleet ship (and even later any warp ship) and lost its luster. Perhaps still used in the classification system, it didn't seem like anything to brag about.
"Canon is only important to certain people because they have to cling to their knowledge of the minutiae. Open your mind! Be a Star Trek fan and open your mind and say, 'Where does Star Trek want to take me now'." - Leonard Nimoy