Your video quality actually looks decent so I wouldn't worry necessarily about a new camera. You need a way to record decent quality audio and then sync it durring editing. There are lots of options out there, ranging from the incredibly affordable and simple to totally professional and outlandishly expensive. The sky is the limit. If I were you, I'd assess your needs when it comes to audio. Do you want to be able to record with multiple microphones or just a stereo pair? Do you want your recorder to be self contained or computer based? Is mobile recording (recording on the go, regardless of location) something important to you?
If you're going to make the investment in recording gear, even a very simple product like the Zoom H2, you want to make sure it will fit your needs in as many ways as possible (not just for audio to sync with drumming videos).