I can help you a bit with the Prowd's in Australia. As a Doolan, we have quite close links.
You mention your grandmother had two sisters, however I wasn't aware of Dorothy but I do have four other siblings (Beatrice b 1893, Brice b 1894, Frances Dorothy b 1891, William b 1886). Both of her parents Charles and Elisabeth Christie were born in Australia, you have to go back a further generation before you end up back in Ireland.
Her grandfather William Prowd was born in Tipperary, probably in 1816 and he married Mary Doolan of Shinrone, Offaly (b 1818) in 1847. They emigrated to Australia, I have found the records but can't put my finger on it right now. As you state, William was a farmer in the Waverley area, a significant landholder at the time. They ended up moving into country Victoria and I've visited the cemetary at Bonnie Doon where many of the Prowd graves are found. I took photos of quite a few so feel free to email off-thread on email@example.com and I'll see what other info or pics i have around the place.
My direct descendant, Nicholas Doolan (the brother of Mary - William Prowd's wife) emigrated to Australia in 1851 but his wife and one of his three children died on the voyage. He ended up remarrying Jane Prowd (sister of William) and having another 10 kids.