Was Rahab's brief confession of faith enough to make her a believer?

Yes. Though brief, Rahab's confession was sufficient for her to become a Gentile believer. She acknowledged that the Lord had given them the land, that terror had fallen on the inhabitants, and that they had heard how the Lord dried up the Red Sea.

Les calls Rahab's statement in verse 8 her confession of faith. He explains that it wasn't much, but it was enough that she became a Gentile believer, one of the exceptions in the Old Testament. She confessed, "I know that the Lord hath given you the land," and that all the inhabitants fainted because of them. She also said, "For we have heard how the Lord, Jehovah, dried up the water of the Red Sea when you came out of Egypt." Les notes that this was forty years earlier, yet they had not forgotten. Before this, she had hidden the spies on the roof with stalks of flax and sent the king's men on a wild goose chase.

Joshua 2:9

And she said unto the men, I know that the LORD hath given you the land, and that your terror is fallen upon us, and that all the inhabitants of the land faint because of you.

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How much faith did Rahab need to become a believer?

Rahab needed only a small, simple faith. Her confession was not much, but it was enough for her to become a Gentile believer. She believed what she had heard—that the Lord had given Israel the land and had dried up the Red Sea.