Before I got my CGM, I used to just let the pump free-float in the bed at night. Some people put it under their pillow. But that also depends on how active you are during sleep! My pump fell out of the bed sometimes, but didn't budge the infusion set.
Now that I have the CGM, I clip it to my pj bottoms, so it will stay close to the sensor. I'm a side and tummy sleeper, so I put it on the side I'm not sleeping on. I'm also a light sleeper, so I switch it to the other side when I turn over, but I doubt your little one could do that -- children are notoriously heavy sleepers!
During the day, I almost always wear pants or skirts, so simply clip it to the waistband. I also have a dress that has a pocket, and I opened the inside seam of the pocket and run the tubing through the hole, so I can take the pump out of the pocket and put it right back in when I'm done. But I'm also not shy about clipping the pump to the neckline of a dress, and if that's not possible, I have a leg thing that goes around my upper calf.
For a child, the most important thing, I think, is not to interfere with activity, so maybe a "fanny pack" or some kind of waist-band case might be the best. There are lots of companies which make such items -- don't know any offhand, but I'm sure you can google Insulin Pump Cases.