I have flown a few times with babies and amazingly the headsets work great. Here is a picture of my niece that I took yesterday while flying up to West Yellowstone. She is 6 months old and the headset works fine. I tried the kids headphones on a 1 year old but my old David Clarks actually work better. Paige (in the picture) is also a very small baby and it still fit her. If she is sitting up you have to hold the headset on. Not too sure how earplugs would work. I know from lots of personal use on motorcycles that unless they are placed just right they don't do much good. With a headset, as long as the ears are inside the cups you know she or he is protected.
This shot was taken on the ground. You can see the gap on the top of the headset. During the flight, she actually slept 95% of the time but had to hold them to her head when she sat up during our final approach.
Can you believe the "First Flight" gear! I swear that child has more clothes than anyone.