Dude, this is so easy it's unbelievable. BTW, you should upgraded her machine to 10.2 just cos its way better than 10.1
If you want everything on both Macs to be available then make an admin account on both machines for the other person.
To do this, open System Prefs, select Accounts (or the 10.1 equivalent). Make a new user, set up the same name as is used for the other machine. Also select the box that makes that user as an administrator. Close that section.
Go to the Sharing pref and switch on Personal File Sharing. Close that section.
To connect to the other machine, you need to know the IP address or the name of the machine. Open the Network pref. Under the TCP/IP tab you will find the IP address assigned that the machine. Alternatively, under AppleTalk tab, you should see the name of the machine. Either should work.
Now you should be able to connect to the other machine. In the Finder, under the Go menu, select Connect to Server. The window that appears may have the other machine already visible. Otherwise, type in the IP address or name, hit Connect and the drive on the other machine should mount on the desktop.
And as they say in France - you're done!
Of course you may not want you daughter to find all those porn files you have stashed away!!! So if you only want to share selected files available you can restrict access to only your Public folder.
In this scenario, you only need to have file sharing switched on. When she selects Connect to Server in the Finder (under Go), your machine name should appear, which you select and hit Connect. If not, you need to put the IP address or name in and hit Connect.
A dialog will appear where you can connect as a Guest and the drive sohuld again mount on the desktop, but this time only the Public folder will be available.
The latter approach is easier but limits access, so if you want to have files shared then copy them to there.
One caveat is that potentially anyone could gain access to those files, so don't put anything sensitive in there. Now your router has a rudimentary firewall to block that from happening but its hard to know without knowing the setup - and I don't know that much about security of these things.
I prefer the former approach cos it limits access to that Username and password. Guest access could be anyone. Plus it gives the ability to share and add anything to the other machine.
Hope that helps - sorry for the long windedness.
Neil