...although it might be necessary if more than one computer is trying to access the net through one connection. And in many of the newer products, the modem and router are combined..There are really only a couple of things required for a single computer to connect wirelessly to the internet. First, you must have a hardware device which connects you through a cable to the internet. Then you'll need the Internet Service Provider which provides the network service. Whether you use an Internet Service Provider which uses a "cable" connection (basically it's the same thing as cable television) or one which uses a DSL connection, this device is a "modem" which connects to the appropriate wall jack in your house. There are wireless modems, "wired" modems, or combo modems, which will receive the signal from your daughter's computer. ...If there is going to be more than one computer connecting through the modem, then a router will be necessary so that all the various computers can connect easily. Although a router and modem are frequently separate devices, there are some new combo modem/router devices such as the "Gateway" device at: THIS LINK
Although they are not used much, there are also "dial-up" wireless routers..This device plugs in to the telephone jack, then allows the wireless computer to move about the house and still connect wirelessly. Here's a link to one such example:
WiFlyer
http://www.wiflyer.com/
So, you pays your money and takes your choice...
Hope this helps.
Grif