What startling offer did Charlotte make to the crew at the end of part 1?

The story starts in the early summer of 1832, as thirteen-year-old Charlotte Doyle prepares to take a voyage from Liverpool, England, to her family's new home in Providence, Rhode Island. Her upper class upbringing and her education give her a very sheltered and narrow view of life. Charlotte finds herself the only passenger and the only female on the ship, the Seahawk. Repeatedly, people tell her she should not be on the ship, but her escort, Mr. Grummage, insists Charlotte go.

After spotting a round-robin, a sign of mutiny, Charlotte warns Jaggery, who heads off the rebellion and kills its ringleader. Charlotte is distressed when Captain Jaggery and 1st mate Mr. Hollybrass whip Zachariah for 50 lashes.

Charlotte tries to protect Zachariah by grabbing the whip, but accidentally hits the captain's face. Jaggery is enraged and whips Zachariah mercilessly, leading to his death and funeral.

After the captain has withdrawn his protection of Charlotte, she feels compelled to replace Zachariah as a crew member out of guilt. The crew allows her to join them after she successfully climbs up and down the tallest mast. Upon learning of Charlotte's plans, Captain Jaggery strikes Charlotte across the face, and she vows to reveal his cruelty to the courts after they complete their voyage.

Her offer to replace Zachariah was the offer.

Cheers!

She joins the crew

Explanation:

Surprisingly, as the story progresses Charlotte was just a passenger of the voyage decided to join the crew, by putting on the trousers and blouse given to her by Zachariah initially.

This decision was made in her attempt to compensate the crew for her actions, an action which involved whipping Captain Jaggery mistakenly.