Yes, you can file your self-employed Income (for dancing) and claim your child using Self Employed version.
And no- the IRS doesn't just take out from what you made, they calculate the tax due based on your taxable income and deductions/credits. Once you have completed all your income, deductions and credits, your final result will show your tax due or refund for your 2016 tax return.
When going through your dancing income, be sure to report any expenses you have incurred and paid for dancing. The net income (your dancing income minus your expenses) will be subject to self- employment income tax, but the amount is included in your Federal refund/tax bill.
More information on self-employment taxes:
https://turbotax.intuit.com/tax-tools/tax-tips/Self-Employment-Taxes/The-Self-Employment-Tax/INF1202...
Note: If you have a large tax bill this year, consider paying quarterly payments to the IRS for 2017... The above link explains estimated taxes.
