Fantastic image....full of joy.
I have same problem sometimes with backgrounds and i have been told different tips to sort them out, the one i use the most is...if you have photoshop...
Go around him with the polygonal lasso tool, or magnetic tool, right click when you have done, and select refine edge, this takes you to the dog on a white screen and you can adjust the levels to suit, it allows you to keep some of the fur, furry without being too smooth...if this shows too much of the background still through the fur, you could possibly clone in a little fur over top or burn the lighter edges to take the edge of....

Having said all that....sometimes its a nightmare getting the dog to sit for an image in the first place, so you get what ever background is there and im normally happy just to get the eyes in focus like you have and a cracking image of a lovely dog!

I love it, considering all the colours in this picture are virtually from the same palette, each is captured perfectly with no blown bits, the detail in the fur is wonderful and both dogs are in focus which isnt easy, love the out of focus background and the chinese whispers that are going on.....