Yes it is, they do discount 3/4 person in a cabin. Personally though depending on how old your daughter is i would suggest maybe getting a bigger cabin. If she is small then inside cabin is ok for 3. If she is 15yrs like ours then i would suggest a large ocean view as a minmum size.
Yes nearly all cruise lines have cabins that will accomodate 3. This is usually in the form of twin beds which can go together to make a double plus either an upper bunk or sofa bed. The pricing varies considerably from cruise line, but in general usually the first two pay the adult fare and then there is a reduction for the 3rd or 4th person. For instance Royal Caribbean have 3rd/4th person rates but P&O base it on a percentage of the main fare dependant on time of year and sometimes the 3rd or 4th person goes free. Decide which cruise you want to do, then enquire with the very helpful and informative people at cruise co by phoning the number at the top of this page.