You are correct!
Once you have the verb "to do" regardless of person or tense (I do, he did, etc.) the other verb is in the "bare infinitive." That means it's in the "to VERB" form without the "to."
I did VERB.
Do you VERB?
She does so VERB!
He didn't VERB.
VERB doesn't change - no s for third person, no past tense.