The 7805 needs to have a minimum input voltage of about 7.5V. The little 9V battery's voltage will quickly drop to less than 7.5V before the ipod's battery is charged. The little 9V alkaline battery is too weak for this job.
Most "9V" Ni-MH batteries have six AAAA cells inside. The nominal voltage for six cells is only 7.2V to 7.5V.
I just measured a charged (a while ago) "9v' Ni-Cad that has a 20ma load. it is 7.34V. Its voltage was 8.4V without a load directly from the charger.
What brand of 9 V battery are you using?
I have a 9 V Energizer which drops to 7.5 V after I use it for 200 mA load for a while. It is rated only 150 mAh, so it is reasonable.