Wheter a character is exhausted or not when you resolve the quest doesn´t matter as long as he wasn´t removed from the quest by a card effect.
You could commit all your characters to the quest and then play Grim Resolve to ready all characters and they would still all be commited to the quest.
But on your subject: No you cannot ready her in that way. You cannot take actions in the staging step of the phase, only reactions. But you can ready her after you commited her to the quest.
So for the quest phase this would mean:
You can play actions --then commit characters -- then play actions --then the encounter cards are revealed and only reactions are allowed -- then you could take actions -- then the quest is resolved.
Same goes for all phases. You can use actions between individual steps of a phase but not in the middle of a step.