"Can you distribute trust income in January without [the trust] being taxed?"

Yes, provided the fiduciary of the trust makes a Section 663(b) election on the trust's Form 1041. In that event, any amount paid or credited to a beneficiary within 65 days (in this instance on or before March 5, 2016) following the close of the tax year will be treated as having been paid or credited to that beneficiary on the last day of the tax year (December 31, 2015).

Follow the screenshots below in order to make a Section 663(b) election in TurboTax Business.