Surely there is not right or wrong answer to this and it is just a case of looking around and being aware, considerate and respectful of other people?
Any spouse or other family member/close friend should be able to attend medial appointments to support the patient without judgement and often this will mean that small children have to tag along but if there is an obvious feeling of discomfort in the waiting room, then the considerate thing to do would be to take the child somewhere else even just temporarily.
It does also depend on location and department. I was going to start an AIBU recently but was too scared of the flaming 
but it ties in here so I'll share a recent experience:
I regularly attend an out patient clinic for specialist gynae problems. The wing of the clinic I attend takes in women with fertility problems, other gynae conditions, offers counselling and treatment for a variety of things including rape trauma, terminations, gynae cancers, infertility, sexual dysfunction and other things. I will not say the reason why I attend.
Often the women in the waiting room as visibly nervous and stressed. On three occasions in two years I have seen people come in with babies, oblivious to others discomfort as they are paraded around. Obviously the mothers have genuine reasons and every right to be there as everyone else but I do think a little discretion and respect would go a long way.
A couple of weeks ago, I turned up to the most unholy racket in the waiting room. There were two women, one with a child or around three years old who was obviously there to "support" a friend. The child dragged chairs across the waiting room, screamed, tantrumed, threw toys, bashed into other women trying to wait quietly with their own thoughts... The woman who was attending the clinic was clearly embarrassed and perhaps had not expected her friend to bring her child - to be honest she looked in need of a good hug but the friend was too distracted with loud parenting to pay her any attention. Several times the receptionist helpfully suggested that there was a children's play area in the main clinic area and perhaps they would be more comfortable there but the child's mother brushed her off until it all got too much at the point that the child started loudly asking her mother's friend "will the doctor give you a jab? Will it hurt? Will she cut you open? Will there be blood?" and eventually another patient snapped and spoke up firmly but politely to say that the play area is in the main reception and not the specialist area for a reason and these were not really suggestions but demands to remove the child from that area. They left - the mother looked like she was going to pick a fight but thought better of it.
I could have kissed that woman.
Obviously there is a difference between a three year old and a baby and the mother should have at least tried to encourage the child to be quiet or brought quiet toys and books to distract her. A baby's babbling cannot be muffled.
On another day the OP might find that other patients in the same waiting room are charmed and grateful for the distraction of her baby. At the same time, even the grump folk in the waiting room should be a bit more considerate to others, including the babbling baby who, as it has been pointed out may be there as a patient in his/her own right. I suppose this comes down to whether the baby's guardian is visibly tried to reduce the noise or acting apologetic to others rather than encouraging it or seeming oblivious.