If Fiora Peerless has a +1 might buff from Pit Rookie, does that also count towards her might being doubled when she defends or attacks 1 on 1?

Yes, the +1 Might buff from Pit Rookie counts toward Fiora's doubling.

When Fiora, Peerless's trigger resolves, it doubles her current total Might — not just her base printed value. With a buff counter from Pit Rookie, her Might is 4 (3 base + 1 buff), so the trigger gives her +4, making her 8 Might for that combat.

This is consistent with how all passive Might modifiers work with Fiora. FAQ #10971 directly confirms she doubles total Might including equipment bonuses, and FAQ #11168/FAQ #11471 show the same principle applies to other passive modifiers (like Master Yi or Discipline) — they're already factored in when the trigger resolves, so the doubling includes them.