Most likely birth for Wm is in Creswick in 1878, as Wm Hy, son of Wm Hy & Maria (nee BOOTH) (reg 15042).
Wm Hy snr married Maria BOOTH in 1872 in Victoria (reg 1351). His birthplace is Belfast and hers is Huddersfield.
Wm & Harriet's marriage certificate is really needed as a starting point, to confirm the right people.
See Booth famiy info here http://members.iinet.net.au/~gstanden/booth.html