Driving an xfmr - to what end?
What's the purpose of the design. If you want to draw more than a few milliamps, you probably should consider using something like the LM3524 -- this chip can do a few hundred milli-amps, and the frequency is easily controlled by an RC network. It's kinda the low end of switch mode power supply design chips, motor control, but works. You can control the duty cycle of the chip by drawing from an internal reference voltage pin and feeding it into an internal amp. They cost less than $0.50 if you shop around.