No. It needs to be carefully gone into or, possibly, gone into with care.If an issue needed to be considered carefully, could I say "This issue needs to be gone into with carefulness"?
It's wrong."With carefulness" is garmmatically awkward?
You're going to be surprised what's new in dictionaries!!
Given that it appears in all those dictionaries, I certainly stand corrected about its existence but I don't think I've heard it used! If I were asked to come up with the noun related to "carefully", I would just say "care".
He did it carefully = He did it with care. I wouldn't use "He did it with carefulness".
It's wrong.