many places that sell beams, either LVL or I Beams usually have charts and guides that will tell you exactly how big a beam needs to be.
You may also want to give a call to your local building permit dept. Yes, you will probably have to buy a building permit then, and have it inspected but for something like this, that's a good thing. Just think about what might happen if you put the beam in the wrong place or don't support it properly and the second floor collapses after you move in all the furniture. Or in the future when your then 3 year old is using the bed as a trampoline. Guess what... People could get hurt and your home owners Insurance might not and probably won't give you any cash to rebuild.