I have long armed and domestic machine quilted with Minky, as other have said when doing on domestic be sure and spray. I much prefer doing Minky with the longarm machine. I have never had a problem using the longarm to quilt Minky, I just be sure and have the stretchiest direction of the Minky go left and right when loading and use very little pressure if any when clamping. For the design I have used many different pantographs, from Roses to Western and they all worked out super. I have also done a floor length Double sized Deer Quilt (for my son) that used a King size bedding Minky (purchased on vacation because he loved the softness and feel) for the back that long armed Super too.
The slipiness would be a concern also to me for a baby, so would be very careful in the way it was used, though for warmth and softness it would be great. A wonderful bedding or floor quilt.