Should I include the stimulus money my girlfriend recieved for a dependent if I am the one claiming the dependent this year?

No you do not put your GF's stimulus money on your tax return.  You only enter the money you received for yourself.   If you are claiming your child then you can use the recovery rebate credit for the stimulus you did not yet receive for your child.   Your stimulus amount is determined by your 2020 tax return.

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check in 2020, you can get it when you file your 2020 return in early 2021

The Recovery Rebate Credit will be found in the Federal Review section,  If you are eligible it will end up on line 30 of your 2020 Form 1040.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-2020-tax-return

https://www.irs.gov/coronavirus/coronavirus-tax-relief-and-economic-impact-payments-for-individuals-and-families