Choose File > Save Command+S to save your document. Dottie uses the standard macOS document system, so Duplicate, Rename, revert to earlier versions, and autosave all work as they do in other Mac apps.
Documents are saved as .dottie packages. A package keeps everything editable: the canvas size, the palette, the animation speed, and every layer as a separate lossless PNG. It is the only format that preserves layers—when you want a flat image for use elsewhere, export one instead.