Just to save you the hassle of the search, the 'Dog Barking' is the Power Transfer Unit for the hydraulics. As you start up the #2 engine the PTU powers up the green hydraulic system as the #1 Hyd pump isn't working at that point. As soon as #1 comes online the PTU stops 'barking'.
Or as the Cabin Crew once told a passenger, 'don't worry, it's only a dog we couldn't catch, it's ok though it'll freeze at 38,000 feet'
W2P