Suzuki 4WD Club of Victoria

so today my battery put out around 9v then it turnes the engine over (just) and across the terminals i still only got about 9.? volts so im thinking my alternator is cake. i put the batter on charge for most of the day and im getting 12.7 or 12.8 now with the engine off so im thinking the battery id still ok. ill check tm tho.
thoughts?

got 12.6v a day later with car off and same when car running. dropped to 12.2 when lights turned on

i brushed downthe terminals and stuff toightto nake sure that a weak earth isnt deterring any flow. maybe a long shot but i dont want to get another alternator if i dont need to