Um, that's not quite how it works.
A fertile egg looks the same as an infertile egg when you candle it, forever, if it stays in the fridge or on the counter in a normal-temperature house.
And egg needs to spend a week or so in an incubator (or under a broody hen) before it will start showing...
White spots or brown spots just happen sometimes. No particular breed is known for laying eggs like the one you have--spots usually get ignored when talking about what color eggs are laid by what breed of chicken.