How to make an online Appointment to lodge my Visa application in Sydney?

You may apply for your China visa through the China visa application service center whose official website is http://www.visaforchina.org/SYD_EN/

I think you have time to get thevisa before your departure, since it usualy takes four working days for the center o process a visa for you, and there is also express service for collection on the third working day and rush service for collection on the second working day.