Well, the "happy" sound you're talking about really has nothing to do with the starting note. All major keys sound happy. All major scales have a the same distance between notes (whole step, whole step, half step, whole step, whole step, whole step, half step), and that can start on any note. When combined with other chords in a chord progression, even minor chords can sound "happy", and those aren't even SUPPOSED to.
But, if you're a more talented musician, there are some very good reasons the key of C may have a happy sound for you:
For people with perfect pitch or people trying to get perfect pitch, C might sound happy because it's very simple to visualize when hearing it. The key of C major has no sharps or flats, and is usually the first scale any pianist learns. The key of C has usually been set into the mind of any serious musician, and the simplicity of it can make them happy.
When studying solfeggio (do re mi fa sol la ti do), when using what we call "immovable do", the note of do is middle C, and the following notes are the corresponding notes of a C major scale. Partly because of this, the key of C Major has become kind of the most known understood key.
Also, for pianists especially, the key of C Major sounds happy just because it's easy to play! It's just white keys with a subdominant of F and a dominant of G, extremely simple to write songs or accompany on the spot with (in comparison to other keys). When musicians hear a song in C Major, they might feel happy because it's an easy key!
That's probably waaaaay more than you wanted, but I hope you can get something out of this!
Oh, and just to clarify things, when you play a song in C Major and then transpose it to any other major key, it will sound just as happy because there really is no difference in the happiness of any major key.