Your post states she's 1 and from the 5 foot description, I'm guessing in her teens. You're in a precarious postion, where many people would take and hands off approach because it is the safest.
If you really, I mean really itend to intervene, you may loose a friendship and possibly save the child. The mom seems to either be existing with herself so far in denial or just plain abussive to allow it to continue, or not sharing the medical condition which may already be known (far fetched though).
I have a daughter with an eating disorder, so I've been there through the burry by head in the sand bit.
I could't get through to my daughter so I enlisted a friend, to approach my d, who was the one to get her to admit to here purging. If this IS an eating DO, the "victim" will do ANYTHING to protect and hide, keep, their disease. It is their only means of controll. They will Lie, and Lie to protect their disease.... period.
Now, mom not interveining is neglect, regardless of the intent, lack of insight, is neglect. for >5 foot the normal body weight is >80 lbs. NO MD would state this, mom is lying. period.
You are faced with, if you intend to intervene, and live with yourself if you don't.....approaching mom and kid seperately, helping mom understand the needed therapy and treatment... calling child protective services, if mom doesn't get treatment see if there is a "hidden disease" and they don't want to share it.
If you speak to the child, just be upfront, are you making yourself vomit? have you noticed your weak, what did you eat yesterday, did you keep it down, are you stressed and having a hard time dealing with it... are you very sick and the family has decided to keep it a secret?
you are left with very few options; ignoring it, getting involved with a huge mess in which the standpoint from a friend will limit your involvement, or making a VERY difficult, possibly lifesaving call to CPS
I'm surprised you haven't received more advise, most hands off, which is the easiest path, but I don't suspect it to be the right one.
Mind you, I'm writing as a parent of a child with bulemia, so my vision, and advise may be well of the mark. I can tell you I saw the same things in my daughter, and it took my oldest daughter telling me "I think .... is throwing up after each meal"... to knock my butt from denial into action as well as a best friend who was trusted by my daughter to approach her and she admitted to her actions.
again, I may be off my rocker (frequently am), but your message is screaming someone take action to me and quick. This is a tough one.... thinking about you. let us know
pm me if you think it'll help