Unfortunately, the IRS generally views dog breeding as a hobby and not a business. You may only deduct hobby expenses equal to hobby income. You cannot take a loss on a hobby.
To enter this in TurboTax, search on "hobby income, loss" and click the jump-to link to go to the start of that section.
If you believe that you are in this business with a profit motive, you may report the income and expenses on Schedule C, available in TurboTax Self-Employed
See these two articles for more on how the IRS determines if your activity is a hobby or a business: