Little Knit is only just starting to get into playdates, so it's very natural for me to hang around right now. I have always considered playdates as being as much of a chance for me to hang around the mom and get some adult conversation in as it is for Little Knit to play with a child her own age.
So in light of that, I would say any conversation topic that you would approach with someone you want to get to know is fine here.
I've discovered that coffee-date playdates with new moms that I'm just getting to know are very much like those awkward first dates I thought were gone forever.
You bounce around topics, making small talk until you land on a topic that you both find interesting.
Hobbies, kids, spouse, kids, coffee, kids, uhhhhhhhhhhhhhhhhhhhhhm, kids, school, work, and kids are all great topics.
Compliment her blouse or earrings and ask where she got them, mention how adorable her little one's outfit is and ask where she got it, etc.
And I agree with previous posters that it is fine to express an interest in her country of origin.
I've had people inquire very politely about LK's father and where he's from and was he born here or there. It's not offensive to me, nor is it to him.