I am pretty short, and also petite. I used to get this all the time, but around when I graduated college it's mainly been restrained to airports (not sure why people are extra-nosy in airports) and when I am with my parents because they are both very tall.
In your case, I probably wouldn't have said anything. I'd probably take the information and find a way to excuse myself ("I'll have to look at my calendar", "I've got to go but thank you for the information", etc.). My mom would probably correct her but I wouldn't really care either way. In a situation like that I think the person could become embarrassed if they were corrected and it would just draw the subject out longer than needed because they would have to express how sorry they were and "YOU LOOK SO YOUNG!!!1!" If I wasn't going to see the person again, I'd probably decide it wasn't worth the aftermath to correct her and just try to leave ASAP and then laugh about it with my mom, who also witnessed the situation.
When people ask my age, I usually respond with "I'm an adult" or "I'm in college." I don't like giving out my age unless it's required, like at a doctor's appointment. I know for many people it's not a big deal, but I got asked that so much as a kid that it became an intrusive question for me. And, people are usually satisfied by this and it also helps change the topic. I don't mind talking about college with acquaintances, so saying "I'm in college" usually prompts them to ask me a question about that, instead of my age/appearance. Depending on the person/situation, I might also say this in a firm tone of voice, so that they know the discussion about my age is over.
I usually respond to "But you are so short!" and "But you look so young!" with "Yes." And then people look surprised that I'm not surprised - apparently I just woke up with this body today! I might start saying "how good of you to notice!" because I think that might point out that they are being kind-of obvious... and rude by repeating that to me three times in a row. (My brother is 5 years younger than me but we were about the same height for years growing up; he is tall. Once, we were in a parking lot and a woman asked if we were twins. My mom said no. She repeated, VERY loudly, all the way to her car, "I CAN'T BELIEVE THEY'RE NOT TWINS!!!!!!" We still find this story hilarious. It was so over the top.)
I rarely have people go over the top; it usually ends with one of those two responses. I can only think of one situation in which I would have needed to pull out the "this topic is not up for discussion" line if we had not been separated (I was volunteering and this person's group moved to another station). I got questions a lot when I was a camp counselor, and my director told me to frame my answers within a frame of "everyone is different". I found bean-dipping and "I am the adult and we are not going to talk about that anymore" to be more effective though because the kids would become VERY curious about my height and would NOT respond to anything but repeated diversion. I didn't mind their questions but when it got to be the only thing they would talk about with me and led to them questioning my authority it was really annoying.
However, I have gotten the baby voice a few times. I have to admit, I kind-of love when this happens, because the people who use it are just so downright... set on using the baby voice that they just don't get it and it's so amusing. I probably look at youngest maybe 12? So I'm not sure why people talk like this to me anyway, but whatever. Anyway, if this happens, I either ignore them (which drives them crazy because they are being SO NICE and I should appreciate it) or answer their questions with my real answers in a bored tone (again, drives them nuts, because it's not what they expect). Recent example: I had an MRI last week and as I was leaving (with my mom who drove me to the appointment) a nurse who was waiting with another patient started talking to me. At first I was confused whether she was talking to me or not, but then I decided to keep acting bored/confused because she was visibly baffled by my reaction.
Nurse: Oh, did you do that MRI ALL BY YOURSELF?!?!?!?!
Nurse (looks really confused): But wasn't it LOUD?!?!?!?!
She still looked confused and kind-of looked to my mom for help. My mom said something about how I had had them before and she just went "oh" and then we left. Her expression was PRICELESS. We should have honestly just left after I said "No" and not given her any explanation whatsoever. I don't think I was being rude - I was answering her questions. I just took on a bored tone. She didn't ask anything else, so I didn't need to say anything further. (It was loud. But I wasn't going to admit that to her and give her that satisfaction!)
I am going to echo someone else - the way I look makes a big difference, in my experience. My mom asked my hairstylist to give me an "edgy" haircut in 4th grade to compensate for my height, and I have asked my hairstylist's opinion on whether my hair looks "young" since then (for example, straight/full bangs would look young on me). I own jeans/t-shirts/etc. but I have also been dressing slightly "dressier" for everyday clothes since high school. I'm more likely to pair a tank and cardigan with jeans, for example, than a t-shirt. I fit in well when I lived in Europe. I just think it provides an extra edge, and though I like dressing that way I make an extra effort to do so when I am doing something like volunteering with kids or on the first day of class, because it sends an "older" message. I did an "experiment" recently because I was flying a lot and I got a lot fewer comments/questions about my appearance when I was wearing something business-like (turtleneck sweater and skirt) or something showing a bit of cleavage, than I did wearing shorts and a t-shirt. In my experience, wearing make-up also helps. I have had someone at a department store counter help me with finding the right make-up and she was very helpful so if that's something you're interested in but don't know much about, I would recommend that - I think I even told her I wanted to make myself look older than I appeared, to balance my appearance out.
I also think I have a normal facial expression that sends a "don't bother me" message, and I learned how to speak in an assertive, firm voice. Those help as well, especially when damage has already been done.