A person who dishonestly claims to have medical or surgical skill, or who advertises false or fake remedies; a medical imposter. In extended use: any person who dishonestly claims to have a special knowledge or skill in any field [OED]

Affected with nausea, queasy [OED]

Quarter of a pint [OED] about 125ml

Quarter: The upper part of a ship's side aft of the beam; either of the two after parts, one on each side of the centreline. Sometimes with modifying word indicating the side, as port, starboard, etc., quarter. on the quarter: in a direction about midway between astern and on the beam. [OED]

Quart:- One quarter of a gallon; two pints (~1.14 Litres) [CPB]

a fairy in Shakespeare's Romeo and Juliet and later works of English literature

[https://en.wikipedia.org/wiki/Queen_Mab]

County Laios  before the establishment of the Irish Free State in 1922

slightly ill [CPB]

Out of sorts; unwell; faint, giddy [OED]

Strange, odd, peculiar, eccentric. [OED]

quiz: to peer inquisitively at; to watch or examine closely, to interrogate with the eyes, study [OED]

Quiz : To make fun of, mock, or tease (a person); to satirise (a thing). [OED]