Hello!!
Im also bringing my dog from Dublin to Sydney. I found two companies that ship pets from Dublin both of which I got quotes off for my little fella. It all depends on the weight, height and length of the dog. I have a mini Dach and was quoted roughly the same from both of them for around €2500.
One is based in Dublin airport, and it's called airsea.ie and the other is K international. Both were very friendly and helpful. They both send the dog to heathrow animal reception centre first where the dog will stay over night and is flown to Singapore where the plane refuels, i was told its usually about an hour stop, then its on to oz.
I personally or my partner cant bear the thought of leaving our baby behind!!
I hope this is of some help to you!