I believe it's fine to use 32 x 32 px for a favicon. They can even be 48×48 px, or 64×64 px. Since they get reduced to 16 x 16, I tend to make them that size, though.
Those tend to be larger, and I believe they need to be at least 57 x 57 px. Usually a better choice for icons like that is around 114×114 px.