As TheCommuter pointed out, you are referring to a doula. For more information on what a doula is, check out
www.dona.com. This will give more in depth information on what a doula is, what she does, the philosophy of doula work, anything you ever wanted to know about doulas but were afraid to ask.
I will say this, it sounds as if you wanted to work with babies who have special needs. As a birth doula, you would not experience this as doulas normally work with the "normal" of childbirth rather than complications requiring NICU care.
Although it would be slightly beneficial (learning what is "normal" to find out what "abnormal" is), it may not be essential to your long term goals.
I admire your long term goals. I've been a doula for the last 10 years and I currently have a newborn in NICU. We have a neonatal nurse practitioner working with her, and she's been the greatest advocate for our baby. Although it requires a Masters degree, it would be awesome work. She spends so much time with us, telling us exactly what is going on and what we can expect.
If you'd like more info on doulas, you can PM me if you'd like.
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