I'm guessing you meant Arbonne, not Airbonne? I understand it seems expensive - I hope you are getting it at wholesale prices. I use it on my 9 month old who has eczema, too. The results have been so good that my pediatrician has started referring people to me. I think the results are totally worth it.
If it's just not in your budget, please don't use an alkaline product like bar soap. Skin is the largest organ & it is supposed to be slightly acidic to kill bacteria. Alkaline products strip that acidic layer (you know that squeaky clean feeling? not good) and leave your baby vulnerable. Also, please don't use vaseline or other petroleum based products. It's like wrapping your skin in saran wrap. It does not absorb & condition & heal the skin. An exception would be in the case of a severe burn - then you would want to wrap you skin in a protective layer but skin affected by eczema needs to be conditioned & nourished. Also, babies' skin is very thin & as a result, cannot hold moisture for very long so it is important to moisturize - especially with eczema.
Eczema can flare up in response to allergies, too. So I would start taking a look at your daughter's diet.
Hope that helps & if you do stick w/Arbonne, use the pump to wash & remember you really don't need very much. And definitely follow up with the ABC baby oil after bath & lotion in the morning - that's what my pediatrician recommends.