Hi Nadene,
I've not travelled with a 7 week old but I have travelled extensively with my DD from 10 months. I've just done the flight to Sydney from the UK with her on my own, so I can understand your concerns!
I would ask your gp about medication to be honest. I think aspirin isn't recommended for under 12s? I think your DD is young enough not to need sedation, but may need help with the air pressure. This can be dealt with by sucking, either breastfeeding or bottle.
I have a friend who has travelled to the UK from Australia several times with a newborn and each time has been fine, her daughter has mainly slept and been adored by all of the staff.
Are you breastfeeding? If so, that will make your life a great deal easier. If she has any discomfort at take-off and landing, feed her. If you're bottlefeeding make sure you bring plenty of stuff, although the airline staff will help with warming up feeds (check with your airline though, just to be sure).
Book a bulkhead seat with a skycot for your DD to sleep in too (or ask for it at check-in, you will get priority but get there in plenty of time).
Take plenty of changes of clothes and nappies, more than you think you'll need.
I hope this helps, good luck with your trip!