Daycare friend

So my 22 month old has a friend at daycare, which is so sweet. They absolutely adore each other. The bittersweet thing is she's going to be moving to another location come January, so they won't be around each other anymore, which makes me feel sad. I was thinking closer to the time to see if daycare can ask if I'm able to reach out to the other child's parents or if they can reach out to me, as I don't want the friendship to end and it would be nice for her to have a playbuddy when she's not at daycare. I don't know who the parents are of the other child as when I drop my girl off and pick her up, the other child is already there. So I've never met or seen the parents. How can I approach this?