That's a question! Some thoughts in addition to Rai's;
There are reports of some of the Native Contingent being swept away in the Mzinyathi when first crossing on the 11 January but in terms of combat fatalities, I guess it would have to be either a member of the 1/3NNC or of the amaQungebeni, under Mkhumbikazulu, during the action in the Batshe valley on 12 January. Of course, no one could be bothered with their names.
First European to die? Trooper Dixon of the Newcastle Mounted Rifles - drowned while taking an ill advised swim (he couldn't!) in the Mzinyathi on 16 January.
First European to die in combat? Hmmm - I'm sort of looking at Nyezane early on 22 January - so either from the (2) fatalities suffered by the Buffs or, more likely (because they engaged first), one from the (6) officers and NCOs of the 2/2NNC.
But, as always, stand ready to be corrected on any of this!