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