If she has costs e.g. getting to and from her babysitting gigs that her employers aren't reimbursing her for, she could claim her travelling expenses against her income but those costs are unlikely to exceed £1,000.
Even as a self-employed person you can't claim travelling expenses from home to your place of work, or back again.
If the young lady drove from home to a family's house to babysit for the afternoon, then drove to another family's house to babysit for the evening, then drove home, the only journey she can claim as a direct business expense is the one between the two families' houses.
What she needs to do though is to bear her travel costs in mind when she quotes her fees for babysitting and factor in her time to allow for this.
As an example: if she babysits for a family for three hours, and they live half an hour drive away (and half an hour back), she needs to charge for four hours, or make sure the amount she charges for the three hours equates to this.