As long as the dog crate has a bottom, is made of strong wire and latches that would work great. My brooder is one.
Steps:
Bedding- Paper towels for the first 2-3 days or week. From then on, shavings work great.
Light- You can hang a heat lamp from the top, starting at 95 degrees and decreasing it by five a week.
Feeders and waterers- I put 2 chick-sized feeders and waterers in mine. You can find them at any feedstore or online. They should be spread out so the "runts" of the flock have access also. In my experience, best to put two on a side and two in the middle.
Draft Protection- You should put wood to cover up the sides of the brooder for protection from drafts, though the door and top can be left with out the wood. I would also recomment putting a strip of wood all along the bottom to help hold the bedding in place.
Protection From Cocci- Cocci is a disease that mostly infects birds up to thirteen weeks. At fourteen weeks they can be old enough to for the most part resist too much of it. Cocci lives wherever chicks are and in them, and if the environment is kept dry and clean then it shouldn't be much of a problem. I'd recommend putting them on medicated chick feed until they're fourteen weeks if they're not vaccinated, but this is optional. Change bedding often.
This should keep the chicks in and the cats out. Good luck. You should keep them in there for about 7 weeks.
Edited to add: To ensure you more that the cats won't go in, you could put the brooder in a room that they don't have access to.