Don't run the aerator in the deepest part of the pond all year. You could get the water too cold and stress the fish. I'd put the diffuser at 2' depth max for the winter, maybe even a little bit less. You only need 5%-10% max open water.
If you didn't compact the dirt after you dug it out, I'd fill it completely with water before adding any fish. That way if it leaks you can drain it and address the issue without losing any fish. Being that shallow, you need to ensure that it doesn't leak or you might have too low of a water level for the fish to survive the winter.