Hi there, my baby also has bad eczema at the moment. I'm not sure what Emu oil is, but here's what my paediatrician recommended:
* when bathing baby, do not use soap as it will dry out the skin even more
* straight after bath, use a moisturising cream like Cetaphil or Physiogel
He has also prescribed hydrocortisal (1%) to use for 1 week to get the eczema under control. Apparently 1% is very weak and does not have adverse effects on babies. My dad is a dermatologist and agrees with this.
I have been following this advice for the past 3 days and have seen a huge improvement in baby's skin.