The first reference to the Modulator
The first reference to the Q-36, which is referred to as the "Uranium PU-36 Explosive Space Modulator", because Looney Tunes is nothing without its strict canon, is also the first appearance of Marvin himself.
The episode is called Haredevil Hare, and it was first broadcast in 1948; you can watch the full episode at DailyMotion.
Because I have a compulsive need to cite my sources, here's the 2016 book Mars in the Movies: A History:
Haredevil Hare (1948)
Summary: Bugs Bunny is dragged kicking and screaming towards the moon rocket, but when he sees a load of carrots being dumped into the rocket, he changes his mind and becomes the first rabbit shot into space. No sooner does he arrive on the moon than a rocket emblazoned with Mars to Moon Expeditionary Forcelands nearby. It so happens that the odd little pilot of that ship is unhappy that the Earth blocks his view of Venus, so he intends to blow up the Earth with his Uranium Pew-36 Explosive Space Modulator. Bugs foils this plan by inadvertently blowing up the moon instead.
Mars in the Movies: A History Chapter 4: "Invasions From Mars"
The episode you watched
The episode you recall, and which you've provided a video to, is the later (1958) cartoon Hare-Way to the Stars; the full episode is also on DailyMotion.