Prefix or adjective meaning "one and a half"

Solution 1:

Sesqui-.

However, it certainly isn't informal, and is also pretty obscure. About the only use of it is sesquicentennial and sesquipedalian which is at a few removes (it literally means 18inches long but it's originally figurative meaning of using long words is the only English meaning).

It certainly wouldn't go with dozen; one would just say "one and a half dozen", "dozen and a half" or "eighteen".

Edit:

If you really want a word meaning 18 of something, you've got octodecuple, which has been used in mathematics at least as far back as 1816 and probably earlier. But really, don't; unless you're talking about properties of mathematical tuples where octodecuples are interesting in some particular way, it would just be horrible.

Solution 2:

One does occasionally hear the term three-halves.

An on-line search for three-halves yields many results, including

• this image ³
  
• many references to Games of Three-halves, including Three-sided football ⁴, three types of 'football' played in Northern Ireland ⁵
• a theatre performance ⁶
• three-halves as a Superparticular number ⁷
• and numerous other varied references.

The expression three-ha'-pence was in common usage in the UK until 1971 as a common way of expressing 1½d (one-and-a-half pence) in the pre-decimal currency system (1½d = 1/160th of a pound sterling £).

An English three-halfpence silver coin was minted around 1561-1582 during the reign of Elizabeth I. ⁸

British three-halfpence silver coins were produced for use in certain British colonies at various times during the reign of Queen Victoria (1819 - 1901)⁹, as illustrated ¹¹:

_{P.S. In answer to the original question, I would not suggest using the expression three half-dozens unless you want to test your readers / listeners!}