A karaoke parties are fun. Girls may choose to perform by themselves or in groups.
You may be able to borrow a karaoke machine from a parent. Hopefully they will have some karaoke cds to go with it that are age appropriate. Some karaoke machines are designed to be stand alone (with a screen that displays the lyrics) and others require a TV to be connected. Or you may be able to use a game system (like a wii or xbox) with a music related game like Rockband or SingStar.
Another cost effective option if you have internet access at your meeting or camp is to use a laptop with YouTube karaoke songs. If you search on YouTube you can find many lists of karaoke songs such as this one or this one.