Look for a Raleigh Colt or possibly a Space Rider. My bride is just a tad taller than your daughter and cannot ride anything over 17" comfortably. You need to be looking in the 43cm range.
Another possibility would be a folder. They fit a wide range of different sized people. If you want vintage and cool, look for a Raleigh Twenty.
There is are several shops in the Chicago area that are very vintage friendly, as well as a strong group of 3 speed riders. I would suggest posting up on
The ChainLink and asking around.
If all else fails let me know I have a spare Colt or possibly a Twenty that I would be willing to part with, it could be shipped up via Amtrak.
Aaron