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.
It depend on where the baby sitting took place. If in your home then the IRS classifies you as self-employed and you report the income as self-employed income on schedule C. Only businesses issue 1099-Misc forms, individuals do not.
If you babysat in the child home then you were probably a household employee and if the income was more then $2,200 then the employer must issue a W-2 form (See IRS Pub 926 https://www.irs.gov/pub/irs-pdf/p926.pdf) .
If less than $2,200
Household Employee income under $2,200 should be reported in:
Miscellaneous Income
Other Income not reported on a W-2
Other wages (yes)
House Hold Employee.
OR Use the "Tools" menu (if online version under My Account) and then "Search Topics" for "household employee income” which will take you to the same place.