I found this on a site don't know if it is true but it sounds ok.
"The name Bull Arab came about around 26 to 28 years ago, when a fellow by the name of Mick Hodges, living in and around Brisbane at the time , ended up with a mistake litter of pups out of a Bullterrier bitch called Bull and a Doberman dog called Arab. Whilst writing an advertisement in the local paper to sell the pups in a hurry after work, he wrote down Bull Arab pups, instead of Bull – Doberman pups and did not even realise this until his first few phone calls that Saturday morning. A good number of people rang enquiri