depends on the fare rule really , some full fares do not allow anything but direct / one flight number , you would be able to change I would imagine , and pay the difference in fare plus their fee which is usually around USD20.00 for the change , but you should call them first to check on your exact fare rules.
I often travel on full 1st class fares btwn SYD and MRU but still have these type of fare fules applying to certain flt nbrs too . i.e if its an A380 etc
you need to pay anything up to AUD 600 extra.
If its an EK aircraft and its direct it should not be a problem though except the change fee USD20 or thereabouts