My 2p
IMHO When you predict a 0-0 you must not mention the first scorer. If one mentions the first scorer when he/she is predicting a 0-0- draw he/she must not be awarded any points [ ie 0]. If you get the 0-0 scoreline right you should get 4 points.
If you are predicting any other result apart from 0-0 only then you must mention the first scorer. In that situation the normal scoring of 3 points for correct score and one point for correct scorer will apply.