The apparently negative manner that Jesus uses towards this woman is a little surprising, but I think that we remain only on the surface if that is all that we see.

Jesus seems to challenge or even argue with this woman, but I would say that what Jesus is doing is teasing her, drawing her out.  One hint is that the word he uses for "dogs" is a diminutive, meaning something like "puppies" or "furry friends."  He is not putting her off, in my opinion, not rejecting her or arguing, as much as he is calling her to be clear both to him and to herself about her faith. 

This is rather reminiscent of the way that he deals with the Samaritan woman in John 4, another woman and non-Jew: He is challenging her just as he does this Canaanite woman.  In this case John is developing a very profound exposition of the nature of the Messiah and the changes he will bring, especially in terms of the Temple and God's presence to his people, and the Samaritan Woman reacts to his words with intelligence, wit, and a certain assertiveness that Jesus matches in a loving and, again, an almost teasing manner.

Note that Jesus doesn't act this way with men or maybe even with Jews, although he stresses the importance of our prayerful insistence in Luke 11: 6-9, the story of the man seeking bread from his neighbor in the middle of the night.  This could well be that he finds the women / pagans to be more receptive, more hungry for what he has to offer.

I end with a question: does it seem like God is ignoring me, refusing me, or maltreating me?  Or is he lovingly asking me to deal with what he has put in front of me?  Or maybe he is insisting, like a teacher, that I grasp the basics firmly before he can deal with my little resistances?