And the name of the ship invariably has the definite article in front of it.
Have you been on the QE2? = Have you been on the queue ee two?
(I note that the Wikipedia article about the ex-ocean liner, now a floating hotel, does not use the definite article. However, most native speakers would use it in everyday English.)
Note that the number "2" is used for the ship. For monarchs, we always use Roman numerals. The rule about how to say it for kings and queens is always "the second/third/fourth" etc.