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I was in the same position recently just wanting to hatch out eggs from the one chicken. I set 8, then another 6, then another 10, over a period of maybe three weeks. I did a big staggered hatch and got 12 chicks from it in total.
You could either try that, or collect for two weeks then set them all at once. You probably won't get as good a hatch rate as you would with fresher eggs, but you should be able to easily beat the average hatch rate for shipped eggs. Shipping is much worse for eggs than storing, especially if you store them carefully and correctly. I think the advice for storing duck eggs is exactly the same as for chicken eggs. Maybe you could ask on the Waterfowl section of this forum just to be sure...