The Fair Work Commission is able to assist with disputes about the operation of Part 6-4C of the Fair Work Act 2009. The Commission cannot assist with all disputes in relation to the jobkeeper payment scheme.
The Commission cannot assist with disputes about decisions of the Commissioner of Taxation as to whether an employer is entitled to receive jobkeeper payments.
Objections to such decisions are dealt with in the manner set out in Part IVC of the Taxation Administration Act 1953. This includes review by the Administrative Appeals Tribunal, and appeal to the Federal Court of Australia.
For information on disputes about jobkeeper eligibility, see Dispute or object to an ATO decision on the ATO’s website.
The Commission cannot assist where an employer refuses to apply for jobkeeper payments. 
It is not compulsory for employers to participate in the jobkeeper scheme.
The Commission can deal with disputes under the dispute resolution procedure in an enterprise agreement or modern award (see ss.738-739 of the Fair Work Act), but the Commission cannot generally assist with claims for underpayment of wages and entitlements, including payments under the jobkeeper scheme.
You can contact the Fair Work Ombudsman for information and advice about claims involving underpayment.