Can not say much about the actual dating as, as China has already pointed out, attempting to date photographs of young children can be very hard, if not sometimes impossible, indeed. But in this case there maybe a glimer of a clue to go on. Strangely enough I can say more about the photographer than I can about the date.
Jules-Ernest Livernois was born on 19th August 1851 in Saint Zephiren de Courval Canada, and died on 8th June 1933 in Quebec City. He was the son of Jules-Isaie Livernois (b1830 Lower Canada- d 1865 Quebec) who started the family firm of photographers in Quebec at 32 St John Street between 1857-1858 (although there is a report of him starting in 1854), there is an entry in a Quebec directory for the period which states " Mr & Mrs Liverois, Photographer, 32 St John Street". After the death of Jules-Isaie, his widow carries on the busines and a firm entitled, Liverois & Bienveno appears between the years of 1866 to 1873 (although I am unsure of the owners full names and if this is a follow on from the firm started by Jules-Isaie) however later Jules-Isaie's widow goes into partnership with one of her son in law's, Louis Welcome, but the partnership is disolved sometime between 1873 and 1874. It is at this point that her son, Jules- Ernest, takes over from his mother and starts running the family firm of Photographers. In 1890 Jules-Ernest, now going by the trade name of J.E. Liverois, Druggist and Photograher, takes on the Provincial Pharmaceutical Association (Canada) on who should have control on the sale of drugs and chemicals to the public. During his career as a photographer Jules-Ernest became one of the most important photographers of his time recording the growth of Quebec and its surroundings as well as its citizen's. Between 1875 and the 1890's many of Quebec's wealthier elite had their image caught by Liverois. A prolific photographer one collection alone has some 1,500 glass plates that Jules-Ernest took in its archives.
Now for the glimer of a clue. Going by the childs footwear I would suggest that this was taken about 1892/93 as the style of boot with the "wrap over flap" (my wording as I can not find my reference to what it should be called at the moment) was evident at this time in women's footwear and children's footwear usually followed on from the adults styles.(see you just knew I would get there in the end)
hope that the above is of some help.
old rowley
