Hi. Last week I flew to Oz with my 4 year old and 5 month old. We went via Kuala Lumpur. Before DD2 was born, I have flown via Hong Kong and Singapore. So I have used BA, Qantas, Virgin and Malaysia. I had one Qantas fligh where the cabin crew were unhelpful. All the others have been great. However I have always flown business class. If you can afford it, I really do think it is worth it for the extra space, comfort and attention from crew. At least consider premium economy.
At airports, you can feel like you need to grow at least 2 extra pairs of hands. Security can be a challenge. I use a back pack and trunki. I have all liquids in one pocket of the back pack. Take your time and don't worry about the queue of passengers behind you. If they are impatient they should have offered to help you.
Don't be afraid to ask for help. This time I requested assistance to be available at Brisbane airport. That really helped - I had some one to hold our passports, you go through a separate immigration queue and she got our bags from the carousel and pushed the trolley through customs.
Make sure your hand luggage contains various little toys to keep your eldest occupied and have enough nappies, formula etc to allow for delays. This time our flight from the uk was delayed by 8 hours, so we missed our connection in KL, had to stay overnight there ( all sorted out by the airline) and get the flight 24 hours later to Brisbane. Cleaning and sterilising bottles in a hotel room is a total pain in the arse but possible.
I don't think there is much difference between the possible routes you have mentioned (I have not gone via Dubai). Since I usually travel to Brisbane, avoiding the need for a extra change at Sydney was important.