The draft card image on Ancestry lists Sept. 12, 1918, as the date that George Herbert Quilliam registered for the draft which was just two months before the war ended on Nov. 11, 1918.

Here is a website that has a photo of a memorial plaque that has a list of the names of those from White Pine Co, NV who died in the Spanish American War, Philippine Insurrection and World War 1

http://www.webpanda.com/WP_cemeteries/images/memorial_ww1_list.jpg

George Herbert Quilliam's name is not listed on the plaque.

The White Pine County, NV History site (below)
has information that from October 12, 1918 to December 28, 1918 there was a county wide quarantine in an attempt to stop the spread of the Spanish Influenza.

http://www.webpanda.com/white_pine_county/historical_society/wp_hist.htm

Could it be possible that your George Herbert Quilliam fell victim to that epidemic, which is why he doesn't show up in further census records?

Here are the mailing addresses and phone numbers for the White Pine Co., NV Clerk of Courts Office and the Elk City Cemetery if you'd like to contact them to see if he shows up in any of their records.
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White Pine County Nevada Vital Records

White Pine County Clerk

953 Campton Street

P.O. Box 659

Ely, Nevada 89301

Phone: (775) 289-2341
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Ely City Cemetery
Campton Street
Ely, NV 89301 -Cemetery Sexton, 289-4602 or Ely City Hall, 289-2430
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Regards,
Lionel Cottier, Jr.