I emailed a photo of the drawing to Kirk Mueller.
Mr Mueller is an accomplished artist and performer who has an almost twenty year association with Warner Brothers. He is described on the ClampettsStudio website as, "a master of character illustration" and as having "an uncanny ability to step into the Looney Tunes characters...".
A simple Google search will list his many accolades.
Mr Mueller's email response from Nov 1st 2008 follows;
Don't know how i missed your mail...
That's a pretty early arcane Hardaway rabbit alright -
Where'd you find that pic?!
I'm gonna run it by Ruth Clampett to get her take on it.
Her Dad Bob was no doubt embroiled with the Bugs Hardaway thing as he was also in on the early mix of the rabbit.
His personal office in Hollywood in the animation facility on Seward Street (now since changed hands) had a clay/plastic or some early modeling material Bugs prototype in a glass box on sitting on the oversized mantle of the moorish/spanish style room that he orchestrated "Beany and Cecil cartoons out of...
I'll get back to you next week...