The first Qantas domestic flight has left Melbourne Airport since Fair Work Australia ordered a termination of industrial action.

Cheers were heard at gate two at Melbourne Airport's domestic terminal as the final boarding call was made for QF 438 to Sydney.

The flight departed Melbourne for Sydney at 4:08 p.m. (AEDT).

"(This is) much better than we expected, much much better, we're thankful," said Colin Coverdale, who was preparing to board the flight.

Mr Coverdale and his wife Valerie are travelling to Sydney as part of their holiday in Australia from the UK.

Passengers started boarding flights in Melbourne after the Civil Aviation Safety Authority granted the airline approval to fly just before 4:00 p.m. on Monday.

Flights to Brisbane, Canberra and Perth were also ready to fly.

Flight QF46 from Christchurch, the first international Qantas flight to land in Sydney, has touched down and passengers have disembarked.

But many other passengers are still facing delays as Qantas works to clear the backlog.

Passengers who arrived in Sydney were angry at the grounding of Qantas flights.

UK resident Cedric Clifford, who arrived from Christchurch at 3:45 p.m. (AEDT) aboard Qantas flight QF46, said he may think twice before flying with Qantas again.

"The man in the middle is the customer and the customer is easy to lose, but boy is he difficult to get back," he said.

Mr Clifford, who is on a five-week holiday around Australia and New Zealand with his wife Margaret, said the grounding of Qantas flights had created uncertainty.

"The flight was fine but we spent the last two days in New Zealand wondering how we're going to get from Sydney back home," he said.

"It does leave doubt in your mind."

Qantas customer Valerieanne Byrnes bought a Jetstar ticket in Singapore, where she had flown from Paris, to get back home to Sydney.

"The unions have a lot to answer for. I'm sure there's mud on both sides," she said.

Meanwhile, passengers who changed their travel destination, rescheduled flights or had them cancelled as a result of the Qantas fleet grounding are being offered re-booking and refund options.

The airline says customers can get a full refund on tickets valid between 5:00 p.m. (AEDT) on Saturday and Wednesday if they bought them before the announcement that flights had been cancelled.

Refund requests must be submitted by January 31, Qantas says.

Qantas also says it will reimburse the difference for passengers who bought a ticket in the same class with an alternative carrier because of the grounding of the fleet.

Customers can also re-book to an alternative Qantas flight or re-book to another carrier where the airline has a e-ticket agreement.

A spokeswoman for Qantas said customers should call 13 13 13 to find out which carriers are covered under this agreement.

Qantas will reimburse out of pocket expenses of up to AU$250 per night for accommodation and AU$100 for meals and phone calls, per person per day, for people who had travel plans disrupted.

But consumer group Choice says Qantas should offer up to AU$800 compensation per passenger.

"While Qantas offers expenses for passengers already in transit, those yet to travel have been left hanging on for hours on call centre lines, with too many bereft of information or a helping hand," Choice spokesman Christopher Zinn.

Slater Gordon class action lawyer Steven Lewis said there were no grounds for a class action by passengers.

"Given the airline has indicated it is willing to offer refunds and provide compensation, there are no reasonable grounds for a class action on behalf of travellers affected by the airline's grounding," Mr Lewis said.