Is the received pronunciation accent a non-rhotic accent ?

Even the Queen and future King capitalize the name of their language: English. RP has been non-rhotic since about the 18th century.

"The Queen's English" can mean RP, but it can also refer to the correct use of the British English language (written, and spoken, regardless of accent) without use of slang or dialect words. One can speak The Queen's English in a Mancunian, Brummie, or Glaswegian accent.

There is a lot of snobbery surrounding the use of RP in England, with non-RP speakers (particularly those with strong regional accents such as Cockney, Geordie, Scouse etc.) often being perceived as less intelligent than RP speakers, even if the content of their speech is identical. Conversely, in Scotland, use of RP is perceived very negatively.

Note that even the Queen has changed her speech patterns over the years - if you listen to a recording of her voice from the 1950s, for example, and compare it to any speech she has given recently (for example her most recent Christmas speech), you'll realise how much her manner of speaking has changed. This has given rise to a common trope that "even the Queen doesn't speak the Queen's English any more" - a study in 2000 concluded that she was influenced by the speech patterns of Essex (known as "estuary" English, after the Thames Estuary), with the pronunciation of "l" in "milk" (i.e. "miwk") being given as one example of this change.

RP is non-rhotic.

Yes, received pronunciation is also called The Queen's (or The King's) English. It it not non-rhotic.