I'm still new to this myself but my gut instinct is that focusing on postwar Anglophone literature, especially fiction, is your best bet, while identifying special thematic or critical interests that will make it easy for you to work on White--that is, race and postcolonial issues fit nicely with a focus on contemporary commonwealth fiction, including Australian stuff. As others have said, consider broadening your scope--I would argue that mass-communication, modern travel, and immigration have diminished the importance of categorizing postwar literature by place, especially within the confines of a cultural community like the commonwealth. Even if you can't find someone who focuses solely on Australian literature to study under, you'll be able to find plenty of people who'll have theorized the heck out of the commonwealth novel, maybe including Patrick White. If you need to fill in any gaps, you might be able to finagle a grant to study in Australia--which we should all strive for, regardless of our specialty!
Modern fiction is probably already a super-saturated field but you're right that Patrick White is pretty under-discussed in the US (it will be important to ask yourself why that is) so you might have an all-important claim to originality and new-ness in that. At the very least, when presenting yourself to universities, you can package yourself as someone quite willing to teach the ever popular giant undergraduate survey of the postwar novel. I suspect that if economists ran english departments, surveys of the postwar novel would be the only course ever offered, alongside "Sex and Shakespeare" and something about Jane Austen.