If you feel like baby is not satisfied and has fallen asleep you can try to get her to wake up and encourage her to feed from the other side. If baby looks full and milk drunk then I find it's not really necessary. My baby drinks one side each feed as well.
I do pump 30 minutes after I latch to stimulate milk production as well as to increase milk supply. I also hope to keep some as spare so I pump when I can. If you're already producing enough or more than enough, just be careful you might oversupply.
Read more