Yes there isn't any right time for her to deal with this, but at 6 she is completely emotionally and psychologically unequipped to deal with this and process it on her own.
I think the younger DD is 6 - the one that was told is nearly 9 (from the other thread). So a little older and perhaps more capable of processing?
I do agree that the Dad should have been involved but by all accounts (also in the other thread) he was flat-out refusing to even have the conversation - the OP felt it was wrong to withhold the information and was quite upset at being made to continue the deception, so in desperation took this opportunity when it came up.