A Brisbane man has been arrested for allegedly possessing child-like sex dolls, under new federal laws targeting child abuse-related offences.

Terry Dunnett, 44, appeared in the Brisbane Magistrates Court today on three charges and faces a potential 15-year jail term if convicted.

The Queensland Joint Anti-Child Exploitation Team started investigating on January 20 when an anatomically-correct doll was detected by Australian Border Force in a shipment from China.

The man's home, in the western Brisbane suburb of Riverhills, was searched five days later, and another two dolls were allegedly found.

Police will further allege a laptop seized at the house contained child abuse material.

Mr Dunnett was charged with two counts of possessing a child-like sex doll, one count of attempting to possess a child-like sex doll and one count of possess child exploitation material.

He has been granted bail and will next face court in April.

New laws banned the dolls last year, with a number of people now arrested across Australia. ( Supplied: Trottla )

After he was granted bail, Mr Dunnett waited inside the court for two hours before running out of the building with sunglasses on and a black shirt wrapped over his head.

The new laws came into effect last September, as part of the Federal Government's Combatting Child Sexual Exploitation Legislation.

Research by the Australian Institute of Criminology has found that use of child-like sex dolls may lead to an escalation in child sex offences — from viewing online child abuse material to contact sexual offending.

Australian Federal Police Assistant Commissioner Northern Command Lesa Gale said studies had shown that dolls could desensitise the people who used them to the physical, emotional and psychological harm caused by sexual abuse.

"These dolls are not harmless and do not prevent people from offending in the future," she said.