Is there a word for of nouns with the suffix er but have the base of a verb? Ex. Sleeper, singer, swimmer. a type of noun that performs an action. The closest thing I can find is gerund, but I have been told they must end with "ing". I am attempting to perform a translation.
The general term for such nouns is agent noun:
a noun denoting the performer of an action (as writer, inspector, patron, hanger-on)
Note, however, that agent nouns don't always end in er (as per some of the examples in the definition.)
I know of no term for only er-suffixed agent nouns. I suppose you could use the one that I just wrote.
Deverbal noun is the usual term for nouns formed from verbs by affixation which denote a person filling the agent role with respect to the verb, such as the ones you cite.
But the term is not specific to just -er nouns. For example, deverbal nouns can also have an -or suffix: “govern ~ governor”, “activate ~ activator”.
Note that 'gerunds' are not deverbal nouns since they are not formed by affixation of the base form of a verb, but are inflected forms of the verb, e.g. "the killing of the seals", where "killing" is the gerund-participle form of the verb "kill".