May or may not be related but I think it's a pretty close fit:
An unedited transcription of a page 1 article from 28 Dec 1911 Simcoe Reformer.
"The Late Mrs. McBurney
Sunday morning, Dec. 24th, came the close of the long and useful life of Margaret Gordon, wife of Mr. Jas. McBurney of North Bay, formerly of Simcoe.
Death came as the result of an accident sustained by Mrs. McBurney on Friday, Dec. 8. On that day she was working about the house engaged in Christmas preparations and her usual household pursuits. Very near the top of a flight of steps she reached up to turn on the light, and in some way lost her balance, and plunged down the stairs.
Although badly shaken up, she was able to walk to her room, and for a week after that she seemed to improve. Then progress toward recovery creased, and she sank into a state of coma, lying in a stupor for five days before death occurred, from compression of the brain.
Very nearly 7 years ago, Mrs. McBurney was born in Banffshire, Scotland, came to the United States when quite young, and later settled with her parents at Oakland Hollow, Brant county.
For many years, Mr. and Mrs. McBurney lived in Simcoe, were they were very well known and highly esteemed, but of late they had resided in Callendar and North Bay.
Mrs. McBurney is survived by her husband and five children, John, of Saskatchewan, Dr. William of Michigan, James Jr. near North Bay, Mrs. Walton, Toronto, and Miss Mary McBurney, North Bay. One brother, Mr. James Gordon, Cleveland, is still living, and Mrs. Th[omas] Gordon of Vittoria is also a relative.
Interment took place Tuesday afternoon in Oakwood cemetery, Rev. Dr. Dey conducting the funeral service."
The Mrs. Walton of Toronto referred to in the article was Jean Gordon McBurney b. 07 Jan 1867 who was my great grandmother and married to William Ralph Walton b. 02 Jan 1868.
Her mother Margaret referred to above was, as you can see, born in Scotland but moved to the US when quite young (she would have been about 5 in 1839) and later settled in southern Ontario in Brant County which is a few miles from West Zorra. So there is a pretty high probability that your McBurney's are the same as mine. Let me know what your connection is so we can share.