When on 1 ticket/PNR with Emirates, 1h:10min at DXB is no issue. Most likely you will be fine/make it.

In case the incoming flight is seriously late and the gate staff can't delay the departure of the SYD flight (there is a curfew at SYD so flights needs to depart on time in order to make it to SYD before the curfew) you will be rebooked to the next flight and Emirates will take good care of you. There is absolutely nothing to worry about.