Hi - another Australian here just back from Disneyland.
Beverly Hills is about an hour away down a VERY boring freeway (double that if traffic is bad).
If you're just going for a day, then the trip isn't too bad, if planning to go for a couple of days then you should seriously consider changing at least part of your booking and staying in Anaheim. That drive will drive you nuts.
Contact me direct through the website link below if you want some information on our trip.