You should have no problem finding a 700c rear wheel. The only concern is that the inner width of the rim is sufficient to accept a 700 X 35 tire. Here is a website that discussed the issue a bit.

http://sheldonbrown.com/tire-sizing.html

If you can compare what you might buy with what you have and try to get a close match in rim width, then you will probably not have any problems.

If your daughters bike has click shifting, more commonly called index shifting, then a 5 speed cogset in the back will not be compatible. Her wheel probably has a cassette/freehub on the rear wheel and the 5 speed is almost definately a freewheel. If you buy a wheel with a 7speed compatible freehub you can cheaply swap the cassette to the new wheel. You can do this as well with the wheel with a 5 speed freewheel if she has freewheel instead of a cassette but you may have to redish the rear wheel and the axle length on the 5speed wheel may not be long enough. Lots of variables.

I tried to look this particular bike up on the web. If it is the model that is circa late-mid 1990's, then the specs that I found did not list the types of hubs. It only listed them as alloy/quick release. It doesnt mention if it cassette or freewheel and with that era it could have gone either way.

Call Harris cyclery, they may be able to help.
http://sheldonbrown.com/harris/hub.html

as an aside...one of the problems with buying an inexpensive anything is that often the cost of replacing parts quickly exceeds the price of the whole unit when it was new.

-J