Hello James,
Although it is of course possible that there was an actual Southern Star that this model is intended to represent, for my part I would be inclined to say that the model is not based on any real-life prototype, but rather a generic/fantasy 19th century man o' war. The model is rather typical of the sort that are mass-produced to be sold as decorative objects, rather than intended as a scale representation of a real ship.
This should of course in no way detract from enjoying it – if your grandfather likes it, that's all that's needed!
/Mattias