I don't believe there is any connection between your Wilmot Arnold Nuttall and my Nuttall family. But while I have been doing research on my family I have collected info on a number of other Australian Nuttall families. Including Wilmot's.
I don't know if you already have this information, but here's a little of the info I have (which I'm sure is by no means complete).
Wilmot(t) Arnold NUTTALL
b.1873 Vaughan, VIC
d.1925, Melbourne East, VIC
m.1899, VIC to Mary Evelyn WITHERIDGE
1. Mary Ivy NUTTALL b.1900, Flemington, VIC
2. William Joseph NUTTALL b.1901, Ascot Vale, VICd.1965, Parkville, VIC
3. Margaret Irene NUTTALL b.1904, Carlton, VICm.Clarence LITTLE, 1942, Woollahra, NSW
I also have information on Wilmot's parents, William NUTTALL & Jane LANE.
William NUTTALL b.c.1830d.1892, Carlton, VIC, parents: Richard NUTTALL & Sarah Elizabeth WITHAM
Jane LANE b.c.1842d.1925, Sunshine, VIC
1. Arnold NUTTALL b.1865, Camp. [possibly Campbell's Creek], VICd.1865, VIC
2. Alice NUTTALL b.1866, The Loddon, VICd.1866, VIC
3. Irving Witham NUTTALL b.1867, Vaughan, VICd.1941, Heidelberg, VICm(1).Sarah BROWNm(2).Annie Mary RABBAGE(have more info on this family).
4. Lillian Mary NUTTALL b.1871, Vaughan, VICm.William Roberts MOONEY (have more info on this family)
5. Wilmot(t) Arnold NUTTALL(see above)
6. Walter Ernest NUTTALL b.1876, Vaughan, VICd.1938, Melbourne, VICm.Elizabeth Mary Ann STUDSOR (have more info on this family)
7. Alice Maud NUTTALL b.1878, Vaughan, VIC m.James WOOLCOCK, 1903, Subiaco, WA.
8. Rosa Jane NUTTALL b.1881, Vaughan, VICd.1902, St Kilda, VIC (Unmarried)
9. Ethel Eva NUTTALL b.1884, Ballarat, VICd.1905, Ballarat, VIC (Unmarried)
Let me know if you'd like further info on any of these families, or would like to know my sources etc (mostly from the Pioneer and later B,D&M Indexes).
Hope this has helped Josie,