Yes, it is ironic that the whispers of the house grow in intensity as the boy continues to rock on the horse. That is the point of the story - chasing after more and more wealth doesn't bring true happiness, it only makes you want more and more and more. And what better time than Christmas for the whispers to grow more audible? Christmas has become a time of "unbridled avarice" (to quote a great movie, A Christmas Story), and I believe that was what D.H. Lawrence was trying to get across.
Is it "plausible irony"? I suppose it's as plausible as the reader wants to allow it to be. How plausible is it that a boy gets racehorse winners' names by rocking on a toy horse? I think that if we can suspend disbelief to allow for that, then we can also allow for the irony of the whispers becoming louder the more wealthy the family becomes.
I think the links below will help you understand both the themes of the story as well as irony itself. Also a re-read of the story will help it make more sense in terms of its themes and the sense of irony used by the author. Good luck!