“At what age should I worry if my child isn't talking?”

I would look at developmental charts and look to see where your child is based on her months of age, not year of age. What is expected out of a 12-month-old is a lot different than what is expected out of a 23-month-old both of which are 1 year of age. Here is a link to developmental milestones: https://doubletalktherapy.com/milestones/

By age three.

Each child is different. By age one, I'll admit I expect to see some of the following speech milestones: The toddler is saying one or two simple words like "dada" or "uh-oh". At the very least I expect the child to use gestures or sounds to get the parent attention, to show intentional communication in some way. I'd expect her to use sounds and gestures to communicate and get your attention. I expect to see them waving good-bye and imitating speech sounds such as "mmmm". But each child is different. Some may be delayed and others may just be late talkers. By age two, I'd expect your daughter to be able to respond to and ask simple questions, make animal sounds, and have a vocabulary of around 50 words, although pronounced unclearly roughly 50% of the time, and name some pictures in books. There is a range of times when you can expect talking to occur. If you are concerned you can rule out difficulty with hearing with a hearing screen and maybe even see a pediatric audiololgist if your pediatrician thinks that is necessary. You can then read to your baby, talk with your 1 year old and narrate your day, engage them in turn-taking, you talk and then when they make noises you wait and listen and then you talk again-teaching them how conversation works, and then you continue to go from there. Get them assessed if you are worried by a local speech language pathologist and learn from the findings.