Where I, and probably the majority of folkies, learned this song was from the singing of Jean Ritchie (KTrad). Her lyrics were:

Go tell Aunt Rhody,
Go tell Aunt Rhody,
Go tell Aunt Rhody
The old gray goose is dead.

The one she's been saving,
The one she's been saving,
The one she's been saving
To make a feather bed.

The goslings are mourning,
The goslings are mourning,
The goslings are mourning,
Because their mother's dead.

The old gander's weeping,
The old gander's weeping,
The old gander's weeping,
Because his wife is dead.

She died in the mill pond,
She died in the mill pond,
She died in the mill pond
From standing on her head.

Go tell Aunt Rhody,
Go tell Aunt Rhody,
Go tell Aunt Rhody
The old gray goose is dead.