Hi i did the journey from Uk to Melbourne with my little boy on my own about a month ago. It was definitely hard but doable, the first flight was fine as its overnight so hopefully your bub will sleep. I dont know where you are stopping over but the second leg was harder for us as he didnt sleep at all, my little one was 16mths at the time. I downloaded lots of childrens progs onto my Ipad and apps like The Giggle Gang, The little Fox , Peekaboo Farm, Peekaboo Vehicles were really good and kept him entertained a bit. Depending who you fly with they sometimes give you toys for the flight as well. Best to check with your airline before travel.
I would advise making them aware that you are travelling on your own before you travel as they will usually help you a bit more on the flight and at the airport. I used a backcarrier on my jourmey instead of a pram and found it much easier, so if your little one is just 6 months a sling would be perfect.
I took loads of ellas kitchen stuff and they let you through with it no problem. If you have any left when you arrive in oz make sure you declare it and then they will let you through with it. If you have asked for assistance aswell it means you shouldnt have to queue at customs and they are a bit more leniant as long as youve declared it.
I found with jet lag, it took me longer to get over than baby! I put him straight into oz night and day routine and it only took a few days to get back to sleeping properly.
Best of luck, it will be hard but make use of the stewards, i found they were willing to help if you asked, you just need to tell them exactly what you need them to do, even if it is just to hold baby for a few mins.
Hope all goes well.
Goodluck!