I don't know about steel stringers. There are some small-sized classical guitars made in China sold here for about 99 Australian dollars. They seem to have several different names. I don't like the feel of them myself. Of better quality; but still pretty cheap are the Spanish made "Admira" guitars. They make a "Junior" line which are a bit under a meter long and which have a narrower neck than the "standard" classical guitar. I am looking at a full-sized Admira at the moment and while I was in the shop I looked at the Admira "Paloma" which seemed a lot more playable than the Chinese ones. This model is not the smallest. You should look at the "Estudio" or the "Infante". The latter is quite cheap--under 200 Australian Dollars.Don't get one that sounds too bad, or that is too hard to play or he/she will get discouraged.
Murray