Thank goodness she's better!! And yes, under these circumstances, you definitely want to continue giving the prednisone. The fact that she's perked up so dramatically shows that she's been suffering from too little cortisol, and typically this does not correct itself within just a day or two. It can take time for her adrenal function to rebound sufficiently to supply enough cortisol on its own. Your vet is putting Layla on a prednisone "taper," and it's very important to follow the dosing instructions as they've been given. If you stop giving the prednisone cold turkey, you can prompt another crisis. Layla's body has to gradually get used to shifting off the prednisone and resuming making enough cortisol on its own.
I can't tell you how glad I am to hear she's doing better, though. After you've stopped giving the prednisone, then you guys will be re-evaluating how things stand with her natural cortisol production and that will determine when you'd be starting back on the Vetoryl again (but at a lower dose). Some dogs need to start back again rather quickly; others get an extended vacation from treatment.
Marianne