The legislation (Section 284 TCA 1997) states that where plant & machinery is in use at the end of the chargeable period (in your case the income tax year ending 31 December) then the wear & tear allowance is due for that chargeable period. It makes no reference to having to time-apportion the allowance.
Revenue's notes for guidance are consistent with this, stating ([broken link removed] - page 53):
"It should be noted that the allowance is available even if the machinery or plant is acquired and put into use for trade purposes towards the end or, indeed, on the last day of the chargeable period or its basis period. Thus, in the case of a chargeable period or its basis period of 12 months ending 31 December, if machinery or plant is provided and put into use for trade purposes on 31 December, title to the full wear and tear allowance still exists."
This is consistent with the treatment in the year of disposal; you do not get any wear & tear allowance in the year you dispose of a capital item, even if you dispose of it on 30 December.