The government is resisting pressure to phase out the trade, ahead of a review expected to recommend more stringent regulations.
Up to now, both government and opposition were anxious to stay in step.
Wood's call follows NSW Liberal and former health minister Sussan Ley declaring the trade should cease.
On Friday the Agriculture department announced it had suspended the supply of sheep to a Qatar abattoir after seeing footage provided by Animals Australia.
It doesn't need a review to tell you that for the sheep these voyages - even when they go better than this one did - are hell, whatever "standards" are imposed.
How Barnaby Joyce plays things in the next few months will be relevant to Michael McCormack's ability to run a united team.
Demoralised Nationals will meet on Monday morning to replace Barnaby Joyce.