Is she an adult? Why don't you try pulling her aside and telling her how your confidence is being affected? She might not be laughing at you, but perhaps at your song, or maybe something else all together.
I don't know what your voice sounds like, but I think audiences tend to be very kind regardless. If you really want to do this, then do it. I am guessing you have had to sit through plenty of other kid's solos, and now it is your turn.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?