To be more specific, could the carbon dioxide fumes produced in the reaction be harmful to a small child? I don't have a strong background in chemistry, and I was prompted to ask this question when it was suggested by a friend that a mixture of 2 cups of vinegar and baking soda is commonly used to euthanize rodents. I'm aware rodents are more sensitive than humans, but I was concerned that a small child could inadvertantly breathe enough fumes to cause harm. I think it would be a great experiment to introduce children to chemistry if not unsafe. Thanks for any advice or guidance.
A basic safety rule in chemistry is "don't breathe fumes". Maximum waft a sample of evolved gas to the nose with your hand. Given a controlled environment, adequate size vessels and small quantities and adequate ventilation, it could be a good introduction to chemistry. However - start in the way you should continue - safety glasses, safe operating procedures etc.. BTW, red cabbage makes a good indicator for this.
I did this experiment with my kids (2yo & 5yo) outside for this reason. We also tied a balloon around the outside of the bottle to keep it isolated and to watch the balloon grow. But to reassure you, one would need to be in an isolated chamber with concentrated CO2 for harmful effects to occur. Remember that CO2 is already present in our bodies and in the air we breathe too, so concentration is everything.
It's pretty safe. The primary source of damage to people from CO2 is asphyxiation. That means you don't get enough oxygen quickly enough. Its danger is similar to helium. You need ridiculously high concentrations of CO2 for it to be harmful and you need prolonged exposure.
You probably drink carbonated drinks. Do you worry about them killing you when your nose gets close to the cup?
I think the much bigger danger is these chemicals getting in people's eyes. Even then, it wouldn't be super dangerous.
Eye glasses are important, though. Lab coat is not really necessary for safety, but it could preserve clothing.
There was already an answer but I thought this might be helpful.
Depending on the quantities of baking soda and vinegar used, it may be perfectly safe to do it indoors, even. In terms of CO2 at least.