Nah, that'd defeat the purpose.
I agree with Arumih, it's not just a matter of slapping a few notes on a page (whether it be from a computer or a piano or even just your mind) and wallah, you've got a composition.
Who (what) is wallah?
By the way, what is the purpose? You've said that you want to compose a piano piece as a gift for your girlfriend, but I don't believe you've explained why.
[snip]
Try to get Finale Notepad free trial (and if your lucky, a CD torrent).
If you want to compose without learning music, you might be out of luck, but if you learn enough to know the note names on the piano, and what a chord is, then you can use your imagination to make what you think sounds good. Your girlfriend will probably be extremely impressed that you even tried to teach yourself to write a piece on your own.If you can get these down:1- reading piano keyboard2- reading music staff3- understanding note values (quarter, half, etc)4- learning major/minor tonalities5- basic chords (major, minor, mixed)Then you can probably come up with a pretty catchy pop-sounding thing. I know some people who have zero music background, but fiddle around long enough to make something decent sounding.You don't need 3 years composition training, and classical lessons for x amount of time. Just look around online at some of the basic stuff I mentioned, and you'll have some sort of base to understanding what the music you hear LOOKS like on paper. Then go from there!
Because I love her? There's not much more to say that isn't applicable to any gift.