This has indeed been discussed before here, but there isn't a lot of concrete information to go on.
The
Prologue to
FOTR has the best information on the origins of Hobbits, though it isn't very specific.
Quote:
|
It is plain indeed that in spite of later estrangement Hobbits are relatives of ours: far nearer to us than Elves, or even than Dwarves.
|
That says to me that Hobbits somehow branched off from Men early on (maybe from an evolutionary process involving hole-dwelling and their general way of life?), becoming a race of their own.
It goes on to say that Hobbits began in the Elder Days, but since those histories were written mostly by Elves (who were either unaware of Hobbits or thought them beneath notice), how Hobbits "developed" as a separate group of Children of Ilúvatar was by the Third Age totally unknown for certain.
I
would include them as Children, of course. They take a major role in the events of the Third Age, as we all know, and thus, I think, must have been "designed" by Eru with that ultimate purpose in mind.