No, the number of spots a ladybug has does not indicate its age.  If it did, most lady bugs would have only one spot, because few of them live more than a year.  There are many different types of ladybugs, and each kind has a different number of spots.

Some dot have any spots at all.  Some ladybugs are named after the number of spots on their backs.  For example, there are two-, five-, nine-, thirteen- and fifteen-spotted ladybugs.

Ladybugs are not really bugs, they are beetles.  Ladybugs are often bright red or yellow, with lack, red, white or yellow spots.–Dick Rogers