The ways I would recommend involve having a second hard drive (firewire or internal) or partition. Install Panther to a new drive/partition and 10.1 will be left alone on the old one; you can then boot back and forth between the two.
If you don't have access to another drive and 10.1 is on the only partition on the drive, you'll have to backup 10.1 to disk image (using something like CarbonCopyCloner) then copy the disk image to a DVD if you have a Superdrive and it's small enough to fit, or over a network to another machine. Then partition the drive into 2 and restore 10.1 to one and install 10.3 to the other.
Just backup your stuff to a CD/Hardrive, and WIPE your drive totally, and install Panther. I know you wont have any problems. It is WAY better than 10.1