Thomas Mason also had tools used to commit burglary in the boot of his car during the incident on June 8 this year.
Leeds Crown Court heard police officers found the child in a distressed state when Mason was forced to stop his car on the Ring Road at Wortley.
Robert Galley, prosecuting, said Mason was banned from driving at the time of the incident.
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Police officers in an unmarked car became suspicious when they saw him driving along Armley Ridge Road at 7.35pm.
He failed to stop when the officers put on blue lights and sirens and drove at double the speed limit through the Armley and Wortley areas of the city.
Mason also mounted a pavement during the pursuit.
He drove in the wrong carriageway towards oncoming traffic when he reached the Ring Road.
Mr Galley said Mason was forced to stop his car and the officers then noticed the child in a distressed state in the front passenger seat.
The child had been travelling without a safety seat.
The vehicle was searched and a trolley jack, a number of electrical saws, bolt croppers and a balaclava were found in the boot.
Mr Galley said the items are commonly used in the theft of catalytic converters from cars.
The court heard Mason had been caught on CCTV cameras driving off from a petrol station in the vehicle without paying for fuel on May 30.
Mason, 33, of Calverley Lane, Bramley, pleaded guilty to dangerous driving, going equipped for burglary, neglect, having no insurance, driving while disqualified and making off without payment.
He has 35 previous convictions for 85 offences, including burglary, handling stolen goods and aggravated vehicle taking.
Joseph Hudson, mitigating, said Mason pleaded guilty to the offences at an early stage and was sorry for what he had done.
Mr Hudson said Mason panicked and drove away from the officers as he knew he was uninsured to drive.
Mason was jailed for 16 months.
He was also disqualified from driving for five years and eight months.
Recorder Anesh Pema said: "It is plain and obvious that (the child) would have been extremely frightened by what was occurring."
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