Yes if you have an original iPhone then yes you can accomplish your goal.
First it would be best to get a new Mini-SIM / Micro-SIM. Yes, it a single SIM Card that can be snapped down from a Mini-SIM to a Micro-SIM! This way you don't need more than one new SIM and once it is activated in the original iPhone you can just snap it down to a Micro-SIM and put in into the iPhone 4.
There is a rather long thread here that discusses the challenges that some have had trying to make the change:
https://forums.macrumors.com/threads/1124040/
The best option would be to use iTunes activation using a new SIM. Yes, there are other methods but it is a roll of the dice since you are depending on the skills of a random individual instead of an automated system!
1. Restore the original iPhone as "New"
2. Insert a new "unused" SIM ( Mini-SIM size, not a Micro-SIM )
3. Complete iTunes Activation steps using your exiting phone number
Note: in your example you would use your girlfriend's phone number
4. Wait for activation completion email, it may take 6-24 hours on a weekend or even longer!
Note: Doing this will also reset your voicemail and delete any existing messages still on the AT&T servers!
Note: Once you complete the iTunes activation, you exiting Micro-SIM will be deactivated in your iPhone 4 ( your girlfriend's phone will stop working!! ) the phone number moves with the active SIM!!!
So once you get the original iPhone activation email and verify that the original iPhone has the correct data plan: $20 iPhone Unlimited Data plan + 200 SMS Txt messages.
If you did not use my suggestion at the top concerning using a combined Mini-SIM / Micro-SIM card, you need to decide if you want to cut the Mini-SIM down to use in your iPhone 4 or just get yet another Micro-SIM and activate it on your iPhone 4. Yes, you can also use one of the many Mini-SIM trays but that has it's own issues. Sometimes they cause the Micro-SIM to get stuck in the SIM tray while it is in the iPhone so I don't recommend.
Again before you ask: Yes you have to restore the original iPhone as "New" and use a new unactivated Mini-SIM aka SIM for the rest of us. The original iTunes activation process wants to pair the SIM with the iPhone so if you try to reuse an existing active SIM it will not work to get the $20 iPhone unlimited data plan!
You will also not be able to keep the $20 data plan once you move back to the iPhone 4. For many the switch to the $30 iPhone Unlimited Data plan is automatic once the AT&T system detects the SIM is back in an iPhone 3G/3GS/4. You should receive a SMS Txt message telling you that you are on the wrong plan and for most customers the switch is automatic and since it is moving you from the $20 iPhone unlimited data plan + 200 SMS Txt messages, it should move you to the $30 data plan and add the $5 200 SMS Txt plan ( yes, AT&T has removed this option but the backend systems still will add it.
You can check the status by logging into your AT&T Wireless account ( OLAM ) and checking the features. Do bother to attempt to switch the data plans by using OLAM, it will fail. All else, read back through the other tread first to see what step you missed or skipped or did not wait for completion!
However, in some cases the move is not automatic due to your current type of plan with AT&T. Yes, there are specific reasons but that's not relevant for this discussion.
WARNING: If you call Customer Care or go to the AT&T store make sure that they don't screw up your existing iPhone 4 and it's unlimited data plan. Some reps are great and can make any adjustments while others don't have a clue.
Dave
