Hi Ray Orbison wannabe or fan,
If you want the rise-time of the voltage across C3 to be the same, then you simply multiply the value of R1 by the ratio of supply voltages, which is 12 divided by 4.5, so it will be about 12.5K to 12.7K.
If the circuit is activated by the junction of R3 and R5 going close to ground, and you want the same low LED current, then multiply the value of R5 by the different voltage ratio that will be across it (subtracting the voltage across the LED).