Kendra Lorrimor p. 9 should be able to cast 4 1st level spells.
4 = diviner 2, so 2 1 level spells + 2 for 16 Int + 1 specialty school slot.
SB says 3.
You are correct: 2 spells from being a 2nd-level wizard, +1 bonus spell from her 16 Int, and 1 divination-only bonus slot.
We're given a hint at the rest of her spellbook, and since she already has comprehend languages prepared, it should be simple enough to add one of the other first-level spells in her spellbook. I'd personally go with protection from evil given the flavor of the setting.