You really need a proper stepper motor driver such as the Pololu A4988. It will allow you to drive the motor with a much higher voltage which is essential if you want high speed. The Pololu A4988 webpage has a lot of useful information.
The L298 is intended for controlling regular DC motors. Stepper motors are very different and, in my opinion, using an L298 is just a bodge.
In any case you say your power supply can only provide 0.6amps yet your motor needs 1.0 amps - so what do you think will happen? Stepper motors draw their full current all the time, even when stationary.
The voltage figures for stepper motors are largely irrelevant. What matters is that your stepper driver should not allow more than the maximum current. Unlike the A4988, the L298 has no means for limiting the current. A high voltage is necessary to get a stepper motor to move fast as it forces the current up to the maximim as quickly as possible. The stepper driver board then prevents the current from rising above the preset maximum.