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I shoot Nikons for no other reason than I was on their Pro-Staff for years and got a big discount on equipment. If I were buying today, I would buy a Canon. I use a 70-300 Nikon lense for all wildlife and sports stuff and find it adequate. That picture was taken at about 80-yards. The major problem that time of morning is lighting.
Moving objects in low light are hard to get "tack sharp" but you have to try. Focus on the deer and you get slightly blurry background that is stationary. Personally, I love that look. Unusual to catch a spotted fawn and a young buck together.