I've known about children's headsets since the beginning, but these are usually for toddlers and older, not for babies. The most consistent method I have heard was to cut a foam earplug in half to make them small enough for a baby and use that. The doctor said this is OK, but you could have issues with pushing wax far into the babies ear. That was going to be the best I could come up with until now.
I have found two different solutions, but will probably use them both in the beginning to ensure protection. The first is a baby sized ear protection muff. The still look big on a baby, but there have been a lot of reviews saying they worked fine on babies down to 4 days old! We don't plan on taking Katie flying until shes about 3 months old.
The second method is to use swimmers ear plugs. These plugs don't go in the ear canal, but instead are almost like putty and you just stick them in your ear over the canal. As you stick them there, they mold to your ear and stay in place. They are waterproof for swimming, but also provide 20-22 dB of noise reduction, which is almost identical to a passive headset. They are reusable, but I bought a 5 pack anyways since I imagine some getting lost or eaten by the dogs. The only hazard is to keep them away from Katie so she doesn't choke on them, but this is no different than the foam plugs. Michelle and I have both tried them to see how well they work and they seem to work exactly as advertised. I'm surprised at how much noise they block (I'm actually wearing the blue bonzai bear ones right now!)
We'll have Katie start using the plugs and muffs a few weeks before we take her flying to let her get used to it slowly. We plan on using them both at the same time in case one isn't sealing perfectly and is letting some noise in, the other one will work. When my headset isn't on right, I can notice and fix it, but we won't have a way to know with Katie until she starts talking. Below are the pics of Michelle and I trying on the ear plugs.