My 17 year old daughter got a 1099misc from the livestock show, the amount is for 1,750 from winning the calf scramble. who files this amount?

She will if she has a requirement to file a tax return this will be included in her income.  This is likely considered hobby income and will be reported on line 21 of a 1040. 

To do this you will click 

1. Federal Taxes
2. Income and Expenses
3. Scroll down click Show More next to Less Common Income
4. Click Start next to Miscellaneous Income
5. Start next to Hobby Income and expenses

 If she does not have other income that exceeds the filing threshold of $6,350, she will not need to file just to report this income.