Assuming she watches the child in your home, she would be a Household Employee.
It is now 2020. Paying her now would be income for 2020, not 2019. It doesn't matter when the work done, it matters when it was paid.
Because it seems she had no income in 2019, she does not qualify to open an IRA for 2019.
If you decide to hire her for watching your child in 2020, be aware that your State could require State Unemployment insurance, Worker's Compensation insurance, and/or disability insurance. You may also be required to pay her a fair wage and pay her at regular intervals and likely other requirements as well. All of these rules vary by State.
In the event that you are not currently married (such as divorced or your spouse died), that situation would also be subject to Social Security and Medicare taxes.
