Good luck with that one, not at all easy, but no - if you make the background light too bright it'll bleach the dog's outline. It must be only just brighter than the key light, aim for 1/2 to 1 stop max.
Hopefully the dog won't be pure bright white and a bit more creamy but you have a very delicate balance to strike there. Suggest move the subject further from the background to reduce wrap, that also reduces the bleaching effect, or screening off all background outside the image area does the same thing (screen against the background).