What does "a quick conception of all" mean?

Question

He coldly but gently loosened her fingers from about his arm and thrust the hand away from him. "Tell me what it means!" she cried despairingly.

"It means," he answered lightly, "that the child is not white; it means that you are not white."

A quick conception of all that this accusation meant for her nerved her with unwonted courage to deny it. "It is a lie; it is not true, I am white! Look at my hair, it is brown; and my eyes are gray, Armand, you know they are gray. And my skin is fair," seizing his wrist. "Look at my hand; whiter than yours, Armand," she laughed hysterically.

Dose it mean that she think immedietly that she has noun of the characters which mean she is black. For example her hair is brown, her skin is fair and ...?

I want to know in the phrase "a quick conception of all", Dose "conception" means: idea or though? and Dose "all" refer to the characters I mentioned above (her hair, her eyes...)?

This passage is from a story named: Desiree 's Baby by Kate Chopin.

Thanks in advance.

Answer 1

A quick conception of all that this accusation meant for her means a quick understanding or realization of the implications the accusation would have for her; she immediately understood the effects that accusation would bring.

A quick conception 
of
all that this accusation meant for her

"all that this accusation meant for her" = everything that would result from the accusation and the effect all of it would have on her

Answer 2

Her "quick conception" (which you are right in understanding as an "immediate thought") is not about her lack of racial characteristics but about "all that this accusation meant for her"—that is, all the consequences of being thought to be black. She sees at once that she will be banished from her home, family and friends to the outermost margin of southern society.