I don't know any IC that works down to 1.2 volts, but try this circuit. It is called a blocking oscillator and is configured as a voltage boost. I don't know what the output voltage would be, you will have to experiment with values for R and C. If it doesn't work at first, try changing the connection to either the pri or sec.
Texas Instruments' TPS61010 boost converter IC works down to 0.8V, has 100mA or more output current (for a small power amp), is very efficient and has a regulated output voltage. Digikey has stock for $2.48US.