It can be found long before Shakespeare, though not in these exact words.
'It is nought good a slepyng hound to wake.' (Chaucer, 'Troylus and Crisedye,' 1374)
'It is ill wakyng of a sleapyng dogge (John Heywood, 'A Dialogue Conteynyng Prouerbes and Epigrammes,' 1592).
I suspect it is very old - probably goes right back to the days when cavemen and early dogs lived together.