If you give her a nice place to brood with protection and lots of nice soft bedding she should lay her eggs there. then you won't have to look for eggs all over the garden.
I don't know how she got Embden either the gander in my avatar is Embden but no matter that is a beautiful goose and so is the gander. You'll enjoy the eggs goslings and the fun these geese bring your way never a dull moment that is for sure.. lol