Much of the fit of a beanie depends on its brim, or the bottom edge.
If you're knitting a hat in the round, you can put half the stitches on another circular needle and check the fit after working the ribbing. Some people use a separate length of yarn to hold the stitches.
If the ribbing is too loose, change to a smaller needle or smaller size. If too tight, change to a larger needle or larger size.
Best to check before getting too far into the knitting!