Many Hindi verbs are formed with the verb "karna", such as स्वीकार करना (to accept), स्नान करना (to bathe), निश्चित करना (to decide), संदेह करना (to doubt), मज़ाक करना (to joke), to like (पसन्द करना). Verbs (e.g. जाना, देना, होना) help making up other verbs as well.
According to wiktionary and my poor knowledge of Hindi, "doing a work" & "working" are both translated into hindi as काम करना (kām karnā)
Yeah, if I see it again I'll try to report it, because I think "we are doing work" should be accepted. It's a natural phrasing to use in English and is a more literal way to translate the Hindi sentence, since it looks like काम is a noun.
I believe you're right that "we are doing work" is an appropriate translation, but there is no other single verb that means "to work" -- you have to say "to do work" in Hindi. So, although you are right that "we are doing work" is a valid translation, I would argue that "we are working" is usually going to be the more natural translation for this.