Should I install Windows 7 on this PC?

i would not want windows 7 running on a 1GB memory , i think 2gb would be better
XP runs really well on 1GB - so re-install that would be my advice

also the cost of windows 7 is another factor - how much are you paying for a W7 version of the software - you could put towards a new machine

remember all programs installed and any data since purchased will be lost on an fresh install

run the following to see if the computer is win7 ready

Windows 7 Readiness Test
Free Download PC Upgrade Advisor Windows 7 Hardware Programs Issues

also go to the computer manufacturers website and see if they have win7 drivers for that specific system. If there are not drivers, then imo, stick with xp since you could have problems finding the drivers you need.

your mobo is win 7 compatib.u have drivers for her on asrock website.but i
recomand 3-4gb ram.

and i forget .for better performance my advice is to upgrade your procesor.

I managed to put Win 7 Ultimate on a Netbook running XP with 1GB RAM without any issues (I would only try this on my own machines normally, but she wanted to see if it would work). The netbook only supported XP so there were no drivers available for 7, but wanted to try it out just to see really and she was OK with it as failing it we could just reinstall XP back. It works fine and has done for nearly a year now, and actually runs faster than the XP OS that was on there. However, bear in mind that your friends specs are different and depending on the hardware, may require the correct drivers relating to Win 7 OS.
Having said that I would see if you can up your friends RAM to at least 2GB as pointed out by the other comments, especially when trying to run multiple applications like Office, Browser etc plus including the amount of RAM that is allocated to the OS alone.

I too would suggest 1st try running the upgrade advisor Windows 7 Upgrade Advisor - Download - Microsoft Windows

put it this way. I had a 6ish years old laptop (NCE versa M400) that ran windows 7. 512MB of ram. I works fine. bit slow but fine.

if you can run windows vista you should fine windows 7 even better (and faster)

as for windows xp. it is still widely used today, great speed, user friendly, and even has x64 version.