I use YLI Monofiliment thread on most of my quilts including baby quilts. I like to see the texture of the quilting instead of thread colors that compete with the piecing. The piecing is always the star.
I've never had a problem with threads coming loose, and I make sure that the stitches are small enough to prevent tiny fingers and toes from catching on them.
I learned about this monofiliment thread from a class that I took from Harriett Hargrave. She recommended using it for baby quilts too. She was adament that YLI was the best brand to use. It works for me.