We should also acknowledge that, not only did she wait until she was dying to tell Forrest about their son, there’s also every possibility in the world that she was lying about him being the father in the first place.
As far as we are shown, they only had sex one time. Meanwhile she had recently arrived afteryears of a destructive and careless lifestyle including sexual promiscuity. And after they had sex, she left the next morning. It’s not impossible, but the odds that her pregnancy resulted from her one night with Forrest, rather than her sexual partners before (or after) she showed up at the plantation, are pretty low. Especially given Forrest Jr. did not inherit any of Forrest’s mental handicaps (an is in fact of higher than average intelligence).
The odds that she was dying, didn’t have any clue who the actual bio-dad was, and so lied to and used her handicapped, lonely, yet wealthy childhood friend as a means to secure her child’s future regardless of his paternity, though, is way higher. None of that is confirmed, obviously, but… it doesn’t look great.