Netbook generally have slower CPUs than laptops (to save on battery life) so will generally be even slower than a laptop.
However none of the things she seems to use it for (email, internet) require a fast laptop so your sure it is not her internet CONNECTION that is slow rather than her laptop.
If her broadband is slow then web pages will take longer to display, emails will take longer to display, making it look like it is her laptop that is slow when it is not.
So buying a netbook, or another laptop, may not make any difference.