Many quail species do not lay white eggs. If the eggs are not white your pigeon may not accept them. The incubation period in quail is different too, or might be, depending on the species. Bobwhite quail take longer to hatch than pigeons; the hen might give up before the eggs hatch. If the...
Here's another idea. If you just would like this bird to raise something consider ring neck doves. My dove raised a pigeon once so I assume that it would work the other way around. Again with the feed mill, but also pet shops; they might know someone who has ring neck doves.
Have you tried local feed mills. They may know a customer that has the type of pigeons you want. Keep in mind that pigeons will not brood much more than 21-25 days; if that. Any eggs that are fostered to this bird has to be close to the pigeon's internal clock and hatch when her own eggs...