I've copied the following from the terms and conditions page of the OV website. The basic answer is, you can go but she can't!!
5. A booking may only be made by a Passenger aged 18 or over. All Passengers who, at the time of departure, will be under 18 years of age must be accompanied by a Passenger aged 21 or over who will at all times during the holiday be responsible for their welfare, conduct and behaviour.
I just had a quick look at some of the websites of the less expensive less formal cruise companies. You could book with island, thomson, Easy. There may be others too, try asking a travel agent who specialises in cruises. Good luck finding somethin.