First, yes there are dairy free probiotics - I just Googled "Diary-free probiotic" and came up with lots of hits. I can't recommend one though, since we use Jarro-dophilus.
It is my understanding that if the mom takes a good probiotic the baby will get what it needs through the milk. However, I've also heard it's ok to open a capsule and sprinkle a small amount on your nipple before baby nurses. I'll be interested to see more responses to this.