You can get wireless routers. These sit by your phone socket downstairs (or any phone socket that's ideally central in your house), and transmit the internet signal wirelessly.
To pick up that signal from your daughter's laptop, it'll need to be wireless capable. Many new laptops have this out of the box already, but if not, you can buy adapters to add this functionality.
Here's a decent one at a good price, which includes both router and wireless adapter:
http://www.ebuyer.com/UK/product/103183