They are USB-powered but I want to play music from my ipad which can't supply them with power so I need a power supply. I was wondering if I could simply use the iPad charger to power the speakers. On the charger it says: "100-240V~ 0.15A (0,15A) 50-60Hz Output: 5V 1A"
Simple answer: yes you can.
Since your speakers are initially USB powered, they are designed to operate with 5V power supply. Voltage of your power supply is exactly 5V and the power is:
Since you only need 1.2W, it should be more than enough to power your speakers.
But you would obviously need to do all the soldering yourself to pick correct wires from charger connector and feed the power supply to the speakers.