They definitely need a cycled tank. Even though the breath air, they have permeable skin. Ammonia and nitrite can burn or irritate their skin. It also stresses them and can lead to bacterial infections.

Cycled media or substrate from another tank will help speed the cycle, but it will still take several weeks to completely cycle.

They will love the 40 breeder! It is a great size for them and offers a large footprint. Remember that in order to cycle, you will need a source of ammonia. If you add the cycled material without adding a source of ammonia, the bacteria will die. Personally, I do fishless (frogless) cycles using Dr. Tim's ammonia chloride. When your tank can convert 2 ppm ammonia all the way to nitrates within 12 hours, then it's ready for frogs.

We would love to see pics of your tank once finished! Good luck!