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This is pretty common with prednisone use. Over the next few days, you will start to see some improvement as her body gets used to the drugs. Keep in mind that pain can also cause what you are seeing.
Since she is eating and drinking, this is a good sign.
The lethargy will start to resolve within the next few days. If it doesn't, you should give your vet a call and see if he has more suggestions. He might even want you to taper off the meds early.
Let me know if you still have questions.