Short answer: no, they don’t exist.

You have two ways of answering a question :

Answer shortly:

• Oui/D’accord/OK (informal)
• Non/Pas maintenant/’Peux pas (informal)

Use a verb

You have to repeat the verb (or use a synonym) just as you did in your example.

If you are asked to perform an action, you can also replace it with a “generic” action verb, and use the tense to modulate your answer:

• Je m’en occupe. (I take care of it.)
• Je vais le faire/Je vais m’en occuper. (I’ll do/take care of it (shortly).)

In this case, you can drop the yes/no.

Rule of thumb

Indeed, using an English-style answer might be formal. My advice would be:

• When answering a yes/no question, just use a simple yes/no answer, and elaborate if need be, but don’t bother repeating the verb as in English. This is not incorrect, just unusual.
• When answering an order (“Take out the trash.”), use one of the examples I gave you (“Je vais le faire.“)