depends -
The issue is whether you need to file a return or not -
If you do need to file then babysitting income should be reported on a Schedule C - which is used for self-employed people. You'll be able to offset the income by ordinary and necessary business expenses (no commuting). Review Pub 334 https://www.irs.gov/publications/p334.
Keep in mind even if the amount of your babysitting income is lower than your standard deduction you'll still have to pay self employment taxes on the net number. So if you earned $3,000 in net babysitting income you'll have to pay taxes equal to around 12.5%. But you might be eligible for the earned income credit.
