My daughter currently can and she is 21 months old. What is an typical age for this milestone?
21 months is pretty spot on, or even a bit earlier than a lot of the kids I've seen. You don't mention how consistent she is about it (gets them in the correct order every time, doesn't skip numbers), but if she is not only able to count to 10 but not mix them up or skip some, then I think that is great!
Here is a nice article detailing how a child moves from no clue, to memorizing the number sequence, to actually internalizing the concept of numbers.
There are different ideas of "counting"
- Memorizing 10 words in a row. If they started to speak early and practice a lot, they can manage it when they are about two years old.
- Being able to count the number of items/fingers etc. My daughter and her friends started doing this correctly when they where four years old.
There can't be such thing as a "typical age" for this milestone (I mean, more precise than "about 2 years old"). Keep in mind that toddler's vocabulary is quite limited :
mean [Language Development Survey] vocabulary scores at 24 months have been between 175 and 195 words, with standard deviations in the range of 70 to 80 (Klee et al., 1998; Rescorla & Alley, 2001). [source]
This means (roughly) that about 70 % of children know "between 100 and 280 words" at 24 months — and 15 % more than 280, 15 % less than 100. See the large dispersion ?
Of course you can translate this dispersion into a time dispersion. As a rough guess, most children should be able to speak 100 words somewhen between 20 months and 26 months. But being able to count to 10 would mean that 10 % of the words he knows are numbers !
Given that, and the fact that some parents will put some effort on numbers while others won't mind at all, not to mention the interest of the child himself, there is no way some "typical age" can emerge.
Furthermore, as reminded by arved there is a strong difference between counting as a nursery rhyme and understanding the meaning of numbers.