Beat eggs well; add milk and vanilla.
In a separate bowl, combine rice flour, tapioca starch, potato starch, sugar, and salt. Add to egg mixture and whisk until smooth.
Preheat oven to 350° F. Spray an 8x4 loaf pan and set aside.
Shred one cup of zucchini with a food processor or cheese grater. Squeeze out excess liquid with cheesecloth or press dry with paper towels.