Dragon alignments are listed as "always good|neutral|evil" so I would say it is inherent in the egg. Doesn't mean there can't be exceptions, but generally this should be the case. I would say they are born evil, but can become good.
One option (total house rule) is to "pair up" various good and evil dragons (red and gold, silver and white, etc.) so that if a good person hatches and races a red dragon egg, out pops a gold wyrmling, who will be good.