Is "half-a-dozen" an accepted term?

I suspect that the parent term is "half of a dozen" which is just being shortened to half-a-dozen. But I caught myself using half-dozen earlier today and wondered which of the variants are considered valid. Both half-dozen and half-a-dozen seem odd written out even though they sound fine to my ear.

I found this in Garner's Modern American Usage's entry on half.

half.
A. Half (of). The preposition of is often unnecessary. Omit it when you can. [...]
C. a half dozen and half a dozen. For this noun phrase, either a half dozen or half a dozen is good form. Avoid a half a dozen. When the phrase is used as an adjective, it becomes a phrasal adjective that should be hyphenated: a half-dozen twirlers with the band.

I would say that "one half dozen", "a half dozen", and "half dozen" are all accepted, however someone who is more knowledgeable than I will have to attest to whether any of those is actually accurate from a grammatical perspective.

This Ngram chart has some interesting findings, however. There are virtually no occurrences of the phrase "half of a dozen" in the English literature over the last 400 years, while the phrase "half a dozen" seemed to peak in the early 1900s, decline over the next century, and then pick up again of late. Meanwhile, the term "half dozen" has seen a similar rise and fall as "half a dozen," but with markedly less variance.

The OED actually has a full entry for this phrase:

The half of a dozen; six (or about six). Const.: see dozen.

a.    1829 T. L. Peacock Misfort. of Elphin vi, Some half-dozen‥forgers.    1855 Thackeray Newcomes I. 7 Pointing out a half dozen of people in the room.    1865 Derby Mercury 15 Feb., I‥might have laid hold of some half-dozen at least.    Mod. Would you like another half-dozen?

b.    c 1401 Jack Upland in Pol. Poems (Rolls) II. 69 The cloith of oo man Myȝte hele half a doseyne.    1420–1555 [see dozen n. 1].    1648 Gage West Ind. 12 He offered unto me halfe a dozen of Spanish pistols.    Ibid. 80 Halfe a dozen Hollanders leapt into the boat after him.    1711 Addison Spect. No. 1. ⁋5 Half a dozen of my select Friends.    1843 Borrow Bible in Spain 145 We came suddenly upon half-a-dozen fellows, armed with muskets.

So the phrase "half a dozen" has been standard for more than 6 centuries. Use it at will!