Congratulations on the next big step of your life! As far as the car loan goes, you can’t just take it over from her. If she’s strapped for cash or not making payments, the best way for you to take over the loan is to have her sell you the car. During this transaction, you can take out a loan, which makes you responsible for payments. The lender will require you to have insurance as a legal obligation for getting the car, and you can add your girlfriend to the insurance policy.
If you decide not to go through with this loan transfer, your girlfriend can still add you to her car insurance policy without any issue. Keep in mind that you can also refinance this loan if rates are lower, and you can have your girlfriend add you as a co-borrower or a cosigner. Just remember that you’re on the hook for the loan at this point, so any missed payments can negatively affect your credit.