1" steerer is preferable for a kids bike. They don’t need the stiffness or weight of the 1-1/8" size. What else that means is open for discussion. You may need to design the frame around the A-C height and 35mm-ish of rake to use the BMX forks. OR If you’re confident in your work, you can probably make a fork that would be appropriately light.
Remember fork failures tend to be pretty bad. The first thing to hit the ground is the rider’s face or head.
BMX forks are designed for bruisers to crashing into jumps so, they are heavy and strong.