I have a 60# longbow and my daughter just got her first 15# bow. Would the bottom section of fishing rods work to make arrows from?
No, and it sounds dangerous. You don’t want a long piece of fiberglass or graphite exploding in her face. Arrows are built with strong "spine", meaning that arrows flex when you release them, and you need to shoot the correct spine strength for the poundage bow you are using.
A few arrows are cheap compared with your daughter’s safety.