What age does a cow give birth?

Cows give birth any age, since a cow is a female bovine that has already had a calf or two.

Heifers, on the other hand, give birth when they're ~24 months of age. Since the gestation period is around 9 months or more (by only a few days), a heifer is able to get bred at around 15 months of age.

A heifer that gives birth at 1 year (12 months) of age is a heifer that was bred way too early. These are what we call "whoopsie" heifers; 9 times out of 10 their pelvic area is still too small at their stage of life for a calf to pass through, and thus must have a Cesarian section done on them. Some heifers may be able to produce enough milk to feed their too-early-calf, but most will have to have theirs bottle raised.