About to/Not about to + Will be about to

“Not about to” is pure slang. It is actually “no way I would do that!”

As you've already pointed out,

I'm going to do it. means it will be done sometime, whether it be within seconds, days, or years.

I'm not going to do it. means it will never be done.

I'm about to do it. does mean it will be done very soon, as in within the next hour.

I'm not about to do it. also means it will not be done, but does not refer to a time period at all. Rather, it is usually used more confontationally. For example, if a child asks his mother for some candy, but the child has misbehaved, the mother may reply with, "I'm not about to give you any candy!" which is meant to show her agitation, and also does not tell us whether the mother plans to give her child any candy later, tomorrow, or if ever again.

For most cases, in the positive (saying you ARE going to do something), then "I am about to ..." can be used in place of "I am going to ...", but the negative is not true. "I am not about to ..." does not mean the same as "I am not going to ..."

edit: A phrase that can be used to say, "I will do it, but I will not do it very soon," is I'll get around to doing it or I'll eventually do it or I plan to do it.