An 18-year-old woman who crashed her car south of Perth had been drink-driving with her baby on her lap, according to police.

The woman and her three-month-old baby were not injured in the incident, but were taken to Rockingham Hospital as a precaution.

She had been driving along Spinaway Parade in Falcon about 6:00pm on Wednesday when she ran off the road.

The driver is facing a string of offences, including drink-driving, no authority to drive and failing to have a child under 16 years restrained.