You're still telling us nothing - we need to know frequency and required current - but at those voltages it wouldn't work, too much loss through the diodes.
The Joule Thief circuit has about only 5mA of output current. There are many other voltage boosting circuits with a higher output current.
You forgot to tell us how much current you need. 10uA? 1mA? 1A? 10A? 100A?
To double the voltage you could put the AC leads in your schematic up to the output of an h-bridge which is being driven with a 555. That or you could make a crude inductive boost converter with a 555.
But in either of those cases you are introducing an IC, and you might as well use an uber easy to use voltage doubler IC from Maxim/Dallas Semiconductor. But a lot depends on your current requirements.
Just ran across this today. Not sure if it works, guessing it's more of a battery-killer. Fewer stages should give lower voltages. Not sure how much current you can expect.
*Should have mentioned, guessing the chip is a 74HC240.
The 74HC240 is a buss driver with "high current" outouts when it has a 5V supply. With a 3V supply its output current is less.
I couldn't find spec's about its output current.
I think its output current as a multi-stage charge-pump is very low with poor voltage regulation.
A Joul Thief requires a voltage regulating load like an LED or a zener diode or else the output voltage will be very high and could destroy the circuit connected to it.