You could try Etihad. They fly to a limited number of African Destinations. Closest to East Africa they fly to seems to be Nairobi, Kenya. You could redeem points to fly from Australia to Abu Dhabi to Nairobi.
You could also redeem on South African Airways although you’d most likely have to double connect via Perth and Johannesburg to whatever destination in East Africa. Keep in mind though, that their partner Ethiopian flies to Addis Ababa and so you wouldn’t be able to redeem points on that route. You’d have to buy a cash ticket for that sector or fly to another destination operated by SAA aircraft.