I really dont 'think' it is. Ive seen so many region 1 versions but not ONE version that we can play in Australia. Ive been searching for this for ten years now. A friend of mine just told me she bought it, so I came looking (AGAIN) but then she said it turned out to be a region 1. When the Johnny Depp version of the movie came out I heard that Disney was going to re-release the original 1951 version... obviously that hasnt happened :(
I found a region 4 edition at http://www.jbhifionline.com.au/Product/284735/DUMBO-|-ALICE-IN-WONDERLAND---DOUBLE-PACK It is unavailable. I rang the store to ask if they had an expected arrival date, they have no idea when it will be available.
I've since been told by retailers, including JB HiFi, that it was released in Australia for a limited time but is now back in the Disney "vault" and won't be released again for years. That has to be the stupidest marketing policy I have ever heard of.