Those verbs are called -suru verbs. Almost all stems of -suru verbs work also as a noun, so ~する and ~をする are both valid in almost all cases. It's not so common to insert を for some -suru verbs (e.g. 到着する, 下降する), but をする is natural when the noun is modified even for these nouns (e.g. 予定外の到着をする, 急激な下降をする). You can check whether the noun is also a -suru verb or not in decent dictionaries, as in the explanation in your dictionary
"noun / noun or participle with aux. verb する" . Of course, there are some exceptions, as I wrote "in almost all cases". For instance, 熱する is a -suru verb, and 熱 is a noun, but 熱をする is invalid even when 熱 is modified. Similarly, 恋する, 愛する and 恋をする are all valid, but 愛をする is invalid. These exceptions are not so many, though.
Explanations in other dictionaries;
しょうかい【紹介】の意味 - goo国語辞書
[名] means 名詞, i.e., "noun", and (スル) is スル動詞 "-suru verb", so these definitions show that 紹介する and 紹介をする are both valid. It's "Noun" and "Suru verb" in Jisho.org.
仕事 - Jisho.org