as far as I understand... and I'm quite happy to be corrected ....
"Jumbo quail" are simply big Japanese quail, Coturnix japconia.
Similar to having "large fowl" compared to "bantam" chickens.
this would mean an incubation period of 17 days, give or take.
the white colour is matter of genetics.
the names also apply to colour. Coturnix are also called eg.. japanese, Italian, jumbo, goldens, range, texas, tuxedo, etc etc. but all the same "type"
and bear in mind e-bayers will name for a good sell, rather than be strictly accurate
have a good google search for info (Coturnix) before you commit to buying it now, so you know what you'll be getting!
we have Japs.
their colours range form the "usual" to tuxedo (white breast, like a bird in a dinner jacket!) and range - like a reddish brown all over. their offspring are even more colours, some white with tux spots, some white with range coloured patches. the white ones are yellow as chicks, the others stripey - I love watching their feather colours develop!
As for sexing... quail are sexually mature around 5 weeks old

though I found the boys take longer before they start "singing!"

newly hatched chicks
we found really high fertility, from just 7 birds in total .
but they arent laying now - September is Winter in my quail house! they wont lay again til about February... unless it snows like it did 2010!
I had a quick look on e-bay & was surprised by how many hatching eggs are up for sale.
(Sorry, I dont want to put you off, just make you aware :| )