With most cruise lines YOU will have a problem , never mind your girlfriend.
Most have a policy that at least one person in each room needs to be over 25 years of age. Generally this is done to prevent cruise ships from becoming spring break parties.
Exceptions are sometimes made for married folks under the age of 25.
You will need to check this VERY carefully before you are turned away at the pier.
With Carnival it specifically says that each guest MUST be at least 21 years of age to board the cruiseline, unless otherwise accompanied by parent/guardian who is at least 25 years old.
You may be in luck though. Norwegian cruiselines states in their brochure that I have on me that:
A passenger under 21 years of age must be accompanied in the same or connecting stateroom by a passenger 21 years or older who expressly agrees to be responsible for the under 21 passenger throughout the cruise. If the accompanying adult is not the minor's parent or legal guardian, a notarized parental/guardian consent letter that authorizes the minor's travel and further authorizes medical treatment in case of an emergency must be delivered to an NCL representative at the pier. Failure to produce this letter at embarkation may result in boading being denied with no refund provided.
Word for word, that's NCL's guideline's for people under the age of 21. So if you and your girlfriend are seriously looking at taking a cruise, NCL is your best bet.