Iryna Zaiets fled Ukraine when the Russian invasion began on Thursday, with her mother Olena Kuzmych and nine-month-old baby Oksana, leaving her father and husband behind.
After making it across the border to Poland, the family secured visas and flights to Sydney, but when they went to check in for the Emirates flight from Krakow to Sydney via Frankfurt and Dubai, they were told they could not fly.
Ms Zaiets' sister in Sydney said they would have been allowed into Australia on a direct flight but would have been deported at transit stopovers because baby Oksana did not have a passport.
Olha Lyeskakova told AAP she has heard from half a dozen Ukrainian families with small children who are facing the same problem trying to get to Australia.
"I am the first one but there is a queue of people in the same circumstances and they are looking at me for how to manage all this," she said.
The department of home affairs has been contacted for comment.
Ms Lyeskakova's family is staying in emergency accommodation in Krakow but will not be able to remain there long and she believes they are not safe in Poland.
"If Russia starts bombing and uses nuclear weapons, it will not be limited by a border, it will go to Poland, it will go everywhere," she said.
Friends who are hiding in Kyiv have told her their houses have been leafleted with instructions in case of a nuclear attack.
Ms Lyeskakova said that while the EU was allowing people to cross the border from Ukraine without travel documents, other countries were not.
"The EU will be overwhelmed with Ukrainians who will be willing to depart immediately from Europe to their relatives in Australia, the US or Canada, but there is no legislation in place at this stage to get it done," she said.
The Australian permanent resident said the Ukrainian embassy in Krakow is assisting her family and she hopes DFAT may be able to quickly issue temporary travel documents for baby Oksana.
"We are very thankful to the Australian government, you can't believe how much support there is in this humanitarian crisis," she said.
It comes as federal cabinet's national security committee begins talks to determine further responses to the Russian invasion, including the supply of lethal weapons to Ukraine.
The aid will come on top of the $4 million already pledged to military assistance through NATO's Ukraine trust fund.
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