It depends on the bird. I put very young birds in smaller cages til I am sure they can perch really well. I put folded towels underneath with papers on top. A fall is so upsetting and can really hurt the bird and hurt your relationship with her.
Be sure to ask the breeder if she is perching well. Then notice how she perches yourself. If she's at all shaky, place the perch low with her bowls near her.
Diana's cage is just a tad smaller than your large one and she does fine in it. When she was young I kept her in a very small cage, smaller than your 24 inch one. Those cages with the little plastic bowls that go in the front with a perch right in front of them work well for very young birds. Prevue makes them and also Hagen.
Annie