- We know there is at least one ship crewed solely by Vulcans (the Intrepid) - do we actually know she's the same type as the Enterprise?
Based on actual spoken dialog, we can also conclude the Farragut ("Obsession") and the Intrepid ("The Immunity Syndrome") are as well.
Just out of curiosity, what is the dialogue you're referring to? I don't recall anything from the episodes themselves that would require either Farragut or Intrepid to be the same class as the Enterprise. (For Intrepid, if you're referring to the 400 Vulcans, I'm not sure that's conclusive.)
Of course, I can't figure out why so many people want Republic to be the same class as Enterprise either. Variety is good!
Actually, that's right! Republic belongs on the list too!
Now, to answer your question:
From "Obsession"
KIRK: Ensign Garrovick is a ship-command decision. You're straying out of your field, Doctor.
MCCOY: Am I? I was speaking of Lieutenant James T. Kirk of the starship Farragut.
From "The Immunity Syndrome"
SPOCK: Doctor, even I, a half-Vulcan, could hear the death scream of four hundred Vulcan minds crying out over the distance between us.
MCCOY: Not even a Vulcan could feel a starship die.
From "Court Martial"
COMPUTER: Ship nomenclature. Specify.
KIRK: United Starship Republic, number 1371.