This dealer, discussed in a prior thread, seems to offer a number of smaller basses:
http://www.nahrmannbass.com/
I own a fully carved Romanian "1/2" size bass, purchased recently from Ideal (hightly recommended), which I believe to be a "9/16" in body size and "5/8" in string length (40"). While it lacks the power, depth, and tone of my larger bass (41 1/4" string length, large 3/4/small 7/8 body), it nonetheless puts out enough sound and depth to make me feel comfortable in smaller groups and is much easier to tranport. My advice is to buy what your daughter and her teacher feel is most comfortable for her at this time. Basses are bought and sold every day, some faster and some slower.