I am a woodworker, and I have 2 suggestions.
First, if the legs are sitting directly on the ground you will have problems with them rotting. Get a few square patio blocks and set each leg on one. This will prevent the rot for years, and also prevent the legs from slowing sinking into the ground.
Second, from an architectural standpoint, the most stable geometric shape is the triangle. If you have angled supports on each leg which attach to the bottom of the horizontal lumber you will create a stable construction. Over time, all of the joints in your rabbitry will loosen, and it will gradually become a bit wobbly. The use of screws instead of nails does help that. But, the effects of weathering and seasonal adjustments in the wood will eventually weaken the entire structure. The added use of diagonally set braces will greatly reduce the likelihood of it getting wobbly. A yearly check on the tightness of the screws is a good idea too.
Overall, you've done an excellent job. It looks like you have some experience in building. Congratulations on a job well done.