According to the specs, that model shipped with 512 MG of RAM in one slot plus an empty second slot. It could be upgraded to 1 GB by adding a RAM module in the second slot or a max of 2 GB if the module that came with it was removed and both slots were filled. Check to see how much RAM is in it.
Definitely check the upgrade advisor, but take the results with a grain of salt. I believe you can theoretically run Win 7 in 1 GB, but it wouldn't leave much in the way of resources to run software and it wouldn't be a very satisfying experience unless her requirements are very modest. If the machine has 2 GB, it's probably adequate (assuming the other hardware meets the Win 7 specs). If it has 512 MG, I wouldn't try to run Win 7 on it even if the upgrade advisor says it's possible.
One other thing to keep in mind is the age of the computer. If the upgrade advisor indicates that any components need to be upgraded, think twice about investing any money in that computer. It would be much better spent putting the cost of the upgrades toward a current model computer that already has a new version of Windows on it. Even if you can upgrade Windows on the computer as-is, recognize that you are just buying a little time. The computer is probably at least seven years old and that is past the life expectancy for some of the components (hard disks often go in far less time, monitors often go in that amount of time, and power supplies sometimes fail in that window; other components are just a matter of statistics). The replacement parts aren't necessarily all that expensive, but you'd be replacing the computer piece by piece, still ending up with very outdated technology instead of current capabilities (and a warranty), if you replace it up front.