I was watching Ian Hislop's Age of the Do-gooders on iPlayer earlier (you can watch it on iPlayer until 27 January here if you are UK-based) and he used various words and phrases based on the phrase 'to do good'. One of them was 'do-gooding'. I looked this up in the OED and the word was first attested in the 1930s, when it entered the language both as an adjective (do-gooding people) and a noun (the tax burden of the do-gooding).
This word can sound rather odd to a native English speaker, as the suffix -ing usually is tagged on to verbs, so it would be more intuitive to put -ing on the verb do, rather than the (here) noun good. However, hyphenated words are often treated as a whole unit and behave like single words. Mothers-in-law is the correct plural of mother-in-law, but you do hear and see 'mother-in-laws' (perhaps because it sounds fine to our ears as 'my mother-in-law's visit' is perfectly grammatical).
Apart from do-gooding, the OED also has the nouns do-goodism, do-goodery and the very common do-gooder, as well as the adjectives do-good and do-goody.