A man who stole a car with a toddler inside is also wanted over the theft of another vehicle at a nearby petrol station, Brisbane police say.

The second incident happened just 25 minutes after the car with the toddler on board was taken from a driveway and dumped after the child's mother gave chase.

Police say a silver Ford ute was driven from a service station at Springwood, south of Brisbane, while its owner was paying for fuel about 5.15pm (AEST) on Friday.

It was taken by one of two men who had been refuelling a green Toyota sedan with stolen number plates.

The other man stayed with the Toyota and drove off without paying for the petrol.

Police have released photos of the pair and believe they are linked to the earlier theft of the car with a 15-month-old inside in nearby Woodridge.

They say a woman left the vehicle's engine running while checking her mailbox about 4.50pm (AEST) when a man ran up, jumped behind the wheel and drove off.

The woman gave chase on foot and tried to block the car's way before she was struck at low speed.

The man drove along Kingston Road, Woodridge, south of Brisbane, about 50 metres before abandoning the vehicle and running off through a Marlow Street unit complex.

The woman suffered minor injuries and the child was not injured.

The man is described as being of Aboriginal or Torres Strait Islander appearance, around 180cm tall and of a slim build.