Then [YHWH] sent fiery serpents among the people, and they bit the people, so that many people of Israel died. And the people came to Moses and said, "We have sinned, for we have spoken against [YHWH] and against you. Pray to [YHWH], that he take away the serpents from us." So Moses prayed for the people. And [YHWH] said to Moses, "Make a fiery serpent and set it on a pole, and everyone who is bitten, when he sees it, shall live." So Moses made a bronze serpent and set it on a pole. And if a serpent bit anyone, he would look at the bronze serpent and live."That serpent on a pole is the caduceus [kuh-JOO-shus], isn't it?" I said to myself.
I looked it up.
No, it isn't.
The caduceus has two serpents on it.
There is a symbol that includes a single serpent on a pole. It's called the asclepius:
But the asclepius comes from Greek mythology--or, certainly, the name does.
In the Bible, we find that the serpent eventually becomes an idol, called Nehushtan, that the religious authorities finally destroy (2 Kings 18:4).
Interestingly, there is a record of a Sumerian healing god in the form of a single serpent on a staff from about 2000 BC. That god's name was Ningishita. . . .
For more on the various symbols, their history and uses, I found Dr. Keith Blayney's page on the asclepius of particular interest.