It really depends on the length of the cruise you want to take. If you want a 3 or 4 night cruise then your options are limited to The Bahamas and a couple of Caribbean options. Longer cruises will mean more of the Caribbean will be available.
June is when prices start to rise because it is the summer and that is family cruise season. You will need to consider Carnival, Royal Caribbean, and Norwegian Cruise Line, and that is pretty much it. Bear in mind that Norwegian does allow 18 year olds to drink when in international waters (I think beer and wine only) and it may also require a signed waiver , but Carnival and Royal maintain a 21 year old age requirement on all cruises from U.S. ports with no waivers allowed.
If you are taking a friend of your daughter along I strongly urge you to use a travel agent who specializes in cruises. There may be some guardian issues involved and you don't want to mess that up, which is easy to do if you try to book it on your own.