You can make the backup from your computer and iTunes. It shouldn't automatically sync but if for some reason it tries to just swipe on the iPhone and cancel.
1. Connect her iPhone to your computer
2. Right Click her iPhone under Devices and choose Backup
3. You can doublecheck to make sure her phone was backed up by going to
Preferences -> Devices and looking at the list of past backups. It should show backups for different phones separately, for example Mike's iPhone 3:37PM, Sally's iPhone 2:20PM.
3. Restore her iPhone to a 3.0 Firmware which will wipe the phone clean.
4. Jailbreak using purplera1n/redsn0w
5. Connect to iTunes and choose to restore phone from backup (not set up as new phone)
Normally you would sync with iTunes to get back her apps and music. In this case you should just make a list of the app store apps she has so you can download it later.
(The backup will save her contacts, texts, notes, photos, pretty much everything on her iPhone. However,it will not put music inside the backup file. Usually I believe it saves an index of what music and videos were on it so that you can sync later with iTunes. If she bought her music off iTunes she can always get it back. If her music came from "other sources" you should probably look up a program that can extract music from the iPhone. I don't know if one exists.)
If you ever need to transfer your backup files to another computer...
I'm not sure where it's saved on OSX but
On Vista, backups are saved to C

Users\XXXXX\AppData\Roaming\Apple Computer\MobileSync\Backup
On XP I believe it's C

Documents and Settings\XXX\Application Data\Apple Computer\MobileSync\Backup
Inside you'll see backup folders named like 324324e4343242343223242 etc. Move these entire folders to another computer using the same folder structure and you can restore these backup files using a different iTunes.