Steven Young, 24, is believed to be travelling with his daughter, Sophie, 23 months old.

They were last heard from in Port Stephens about noon on Wednesday, December 31.

Mr Young was described as being of Caucasian appearance, about 180 centimetres tall with a fair complexion, ginger hair and blue eyes.

Sophie was described as being of Caucasian appearance, fair complexion with red hair.

It is believed the pair may be travelling in Mr Young's car, a black, Mitsubishi Magna with a NSW registration of CB 45 TY.

Inspector Matt Meares from the Port Stephens Local Area Command said that police were appealing for information about the pair.

"We have concerns about the welfare of this man and child and believe that they may be travelling or staying somewhere on the North Coast," he said.

"I urge anyone with information about their location to come forward as this disappearance is totally out of character.

"Anyone who knows Mr Young's whereabouts, or has any information that could assist investigators with their inquiries, is urged to contact Crime Stoppers."

Anyone with information can phone Crime Stoppers on 1300 333 000 or Raymond Terrace Police Station on 4983 7599.