Moment that's doubtful on the first of January (5)
I believe the answer is:
jiffy
'moment' is the definition.
(I know that jiffy is a type of moment)
'doubtful on the first of january' is the wordplay.
'doubtful' becomes 'iffy' (I've seen this before).
'on' says to put letters next to each other.
'the first of january' becomes 'J' (the first letter of the word 'January').
'iffy' put after 'j' is 'JIFFY'.
'that's' acts as a link.
(Other definitions for jiffy that I've seen before include "Moment (slang)" , "Split second" , "An instant" , "Very short moment - type of bag" , "Two shakes of a lamb's tail?" .)