No question that a doctor should take a look at her. The sooner the better because a lot of things can be put on the right path with therapy at this young an age.
Now, to bringing it up to her mother:
You do need to talk to her as an authority on young children. You have seen many children and can tell that this girl is different in this one aspect and needs to be evaluated so that it can be corrected, if needed.
Obviously, no mother wants to hear that something might be wrong with her child. Now that she had some time to think about it, she might be more approachable, or perhaps you could have an open door day where she would be able to observe her daughter with other kids and see that it's a bit out of the ordinary...
On the other hand, I don't know the mother's situation, but it doesn't sound like she is going to the regular baby check-ups because a doctor should pick-up on something like this... so perhaps, besides her fear of the unknown, it's her fear of not being able to afford the possible medical care costs... perhaps you might want to innocently ask about her doctor visits (where, who, how often, when is the next one scheduled, vacinations, etc.) to find out if that might be the stumbling block... there are lots of city, county, state and non-profit programs (many for free) available for kids...
Shooting in the dark here, but the girl definitely should get evaluated