The first rocket was a Russian R-7 Semyorka (which was a modified inter continental ballistic missile), known to the West as SS-6 Sapwood and to the Soviet Union as GRAU index 8K71.
It was used to carry Luna 1 the first probe (spacecraft) to reach the vicinity of the moon.
There may have been other rockets that were launched "at" the moon but this was the first whose payload actually reached the moon.
To my knowledge Australia have not launched a rocket to the moon as yet.
The name of the rocket that launched the first people on the moon was a Saturn V, on mission Apollo 11.
Launched by the Saturn 5 rocket (the largest rocket ever built), the first spacecraft to take men to the moon was the Apollo spacecraft.
The first rocket to get near the moon was the Soviet Luna 1 spacecraft in 1959. Later that year, the Soviet Luna 2 spacecraft was the first manmade object to reach the surface of the moon.
Saturn V, a 3 stage rocket.
The first rocket launched as an attack was the V1 rocket, nicknamed "doodlebug
the rocket was actually launched in either China or Russia
The Saturn V.
If a rocket is launched from the moon it will travel faster and longer, as it has less gravity.
the first rocket (the V2) was launched in 1942.
They were launched from earth atop a Saturn V. They flew to the moon aboard their Apollo Command Module and landed on the moon in their Lunar Module.
The Apollo 11 Launched on July 16, 1969, in it was Neil Armstrong and Buzz Aldrin, the first two people to step foot on the moon