Lizzy, I'n not sure if you will get a lot of feedback on this LA/MS limited forum. So you may want to post your question on the Vegetable Garden Forum. Your success is not likely to be related to location, so feedback from other areas will be just as beneficial. And, if I recall correctly, I think there was a recent post on the above forum wherein those responding had good results with their no-dig gardens.

On timing to put out transplants and plant seeds, I'd say go for it. We've had cooler than normal weather lately but it is now may and I expect the pendulum to start moving in the other direction. You did not mention your plant selection but you are probably at optimal timing for some of the warmer weather choices - squash, canteloupe, okra, eggplant, Chinese long beans...

For the cat attacks you might like to try chicken wire. I do have a cat that did like sleeping on the wire, but if you do a few cuts here and there and turn the points up that should take care of that problem. If you are using rows you might want to cut it to fit between the rows? We have a snail slug problem here and I am just learning to use all those ground up egg shells to protect my seedlings.