Unstable output can be a combination of one or more of the followings. Obviously, changing the whole dynamo(the old term, now call generator) will make sure you won't be falling into the trap of treating the head and then the toe needs treatment soon afterwards.
OK, here you go:
carbon brush failure
voltage stabilser failure
magnet/coil failure
bad contact
slipping drive belt
I think it's worth a try. BTW, as battery output is just 12V, and as long as the dynamo can output higher than 12V, your battery will be charged up, only a matter of time. As long as you can start the car I do not think there is a urgent need for repair. To monitor if the dynamo is dead, buy a LED indicator (less than $100) and plug into the cigarette lighter to check the voltage.