Correct me if I'am wrong, Dorothy had Michael when she was about 18 or 19 years old, on the show Dorothy mentioned that Michael now who is 30 years old and yet still not taking responsiblity for his own life, does that mean that Dorothy is somewhere give or take between 48 and 51 years old. If so, Dorothy hasn't aged very well.

This is one of the many glaring continuity gaps in the series, most of which have been discussed here before. There is no way Dorothy was 48 years old during the series. Keep in mind that she and Stan were married for 38 years and divorced by the first episode. Hence, her oldest child being 30 makes no sense whatsoever.

Equally bizarre, Michael's age is given as 23 in another episode!

True, Dorothy was supposed to have been married as a teenager, but the reason for this was that she was pregnant. If she's now 55, then one of her kids must be near 40. Both of her kids appeared on the show at some point, and both appeared to be 30ish.

Wasn't it Kate that was her first-born?

I'm pretty sure she was the oldest, yes.

In my opinion Bea just appears the oldest because of her gray hair, her face really doesn't have many wrinkles. Picture Bea with blonde or brown hair, don't you think she would look younger?