I believe you get the first three new breeds around the same time you're able to get the "better" lures in the Barc shop (not the ones on your walks). I believe this is also about the time that your dog will start picking up new items on your walks. I'm gonna pin this occurrence at somewhere between having 800-1000 owner points, but don't hold me to that. Though, with talking to different people, I do believe I might have that pinned down...
Btw, I posted as a guest before, but I'm the one who gave her email out to you all to contact with questions. It's still firstname.lastname@example.org
if you guys have any more questions! ^^
I'm planning on putting some serious time into this game this weekend so that I can uncover more... If I come across a shocking discover, I'll be sure to put it up here for you all. ^^ Hope my info helps~!