I have two cat carriers. For chickens, I prefer the one with an opening top as well as a door at one end.
Even so, Mary doesn't fit in a cat carrier. She's quite a large hen, up to my knee, and she's wide too. That's why she travels in the picnic hamper, which she has learnt to escape from.
All the hens dislike being handled, so I always carry them standing on my hand (or hands) at nighttime, off the roosting perch. Then I struggle to place the smaller hens into the open top cat carrier because it's rather squeezy with my arm/arms in the way lifting them down into it. And rather squeezy with my arm in the way carrying them through the end door.
So I'm thinking while the cat carrier is sufficient, it's not optimal. And I have lots of leftover ply to make a more sensible travel box with a larger than a chicken side opening, a perch, a dropped floor for shavings. Handles for carrying, or wheels for rolling. Ventilation holes.
Something like this.
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