How do I transfer my old iphone 3gs to a new iphone 3gs with out upgrading to ios 6?

Just sync or Back Up the iPhone, you do not need to Update Firmware or Restore Firmware. Just sync or Back Up.

Then sync or restore the Back Uo to the new iPhone. You do not have to Update Firmware or Restore Firmware. Just sync or restore from the Back Up. Do not Restore the Firmware.

Set Up as New iPhone, do not Restore. Then later you can restore from your Back Up. Do not Restore your Firmware. Restore Firmware is different from restore from back up. Do not Restore Firmware.