Curiously, the OED says:
half-dozen | half-a-dozen
The half of a dozen; six (or about six).
In its quotes, it does not distinguish when it means 6 and when it means ~6.
But for dozen, the OED does not depart from 12.
A group or set of twelve. Originally as a n., followed by of, but often with ellipsis of of, and thus, in singular = twelve. Also, used colloq. in pl., either indefinitely or hyperbolically, for any moderately large number; cf. hundred n. and adj. 2. (Abbreviated doz.)
The OED gives no example of 'dozen' meaning 'about 12'.
Originally dozen was a noun, and so a dozen of eggs meant twelve eggs not somewhere between 10 and 14.
It does say that dozens can mean a moderately large number, just as hundreds can mean a large number.
This is not to get all prescriptive. People can use words in any manner they want. I'm just saying that a dozen equals twelve and a half dozen is six, or 'around six'.
Edit to add that a dozen dozen equals a gross, which is exactly 144, not around 144 or between, say, 122 and 166.