I am currently retired military and disabled. I started making money doing doordash last week. If and when I get a 1099, can I file taxes and get the child tax credit?

The child tax credit for a child under age 17 is based on the amount of income you receive from working, so you might become eligible for the CTC---depending on how much you earn.  If you are just beginning that DoorDash work late in 2024, you are not likely to qualify for much (if any) but you might if you continue working in 2025.     

The child tax credit for 2024 is still $2000, with a refundable “additional child tax credit “ amount of up to $1700.

  The maximum amount of the child tax credit is now $2000 per child; the refundable “additional child tax credit” amount is $1700.   In order to get that credit, you have to have income from working.  The credit is calculated based on the amount you earned above $2500 multiplied by 15%, up to the full $1700 per child. If the amount you earned was too low, you will not get the full $1700.

 If your child is older than 16 at the end of 2024, you do not get the CTC.  But you may still get the non-refundable $500 credit for other dependents instead.

https://ttlc.intuit.com/questions/1900923-what-is-the-child-tax-credit

https://www.irs.gov/help/ita/does-my-childdependent-qualify-for-the-child-tax-credit-or-the-credit-for-other-dependents