"600 wheels"? 650 perhaps? Smaller than 700. A bit harder to find tires for but they are available.
Compared to a Varsity fixie, this would be a delicate bicycle. And a faster bicycle.
Would this be the right tool for the job?
Nicer bike than that heavy-ass Varsity, but it may need more attention, too. She'll probably love it if it fits.
650 tires aren't common but are making a small comeback, thanks partly to Grant Petersen's attempts to revive them. If that turns out to be what it has, and you need some, you can find them at www.rivbike.com. I converted an old Bridgestone of my wife's from 700 to 650, to get room for wider tires, and she enjoys it much more now.