Somethings to try, if you have not already.
1) Make sure you've turned the volume up. The iPad keeps different volume leves for the headphone and speaker, so do expect it to play just because the speaker did.
2) Make sure the headphones are firmly seated. It's easy to think they are, especially if you have a cover, and the jack gets caught on the edge.
3) In Settings > Music, check your Volume Limit setting.
4) While it should not affect Music playback, you should also check to make sure you are not muted. This can either be the slide switch next to the volume rocker, or in the multitask bar (double tap home and slide the icons to the right). The settings are here:
iPad: Understanding the side switch
5) It never hurts to restart the iPad, or reset if that does not work.
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.