I let a couple of geese go broody last year who were about the age of your goose. I monitored them and made sure they were getting enough to eat. They handled it fine as far as their own health went, but the problem was the eggs. A first year goose lays very small eggs compared to later years, so there can be a lot of issues with the hatch. Because of this, I didn't have high expectations. Four eggs did manage to hatch naturally, one of which wad killed when its mom trampled it in her inexperience. I wound up having to throw a fifth in the incubator and helping it out, and those 4 remaining goslings were successfully raised by the flock and made it to adulthood. This year my girls are 2 years old and I let them brood again. Almost all the eggs hatched, and the goslings are noticeably larger and more robust than the goslings were from last year. The people who recommend not hatching first year eggs have good reason for giving that advice.
If you're able to make sure your goose is taking care of herself while she's broody there's no reason why you can't experiment with it and see how it goes, but keep in mind the hatch rate will probably be lower and you may need to intervene since the eggs may be too small for the goslings to maneuver for successful hatching. In fact, hatching first year goose eggs is one of the instances where I'd advise
not listening to folks who tell you not to intervene, because more often than not it's simply the size of the egg preventing the hatch, and not the health of the gosling. That said, I do think not hatching first year eggs is the best course, and to think about maybe waiting until next year to let your goose brood. Either way you choose, good luck!
Oh, and here's a picture of a first year goose egg next to a second year goose egg, just so you can see the difference a year can make in the size (tip: the can is not a goose egg

).
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