This should be fine and is routinely done for many patients. As long as your skin is healed from the peel the Botox is injected in the muscle. Good luck!
It depends on the level, type, and strength of the chemical peel. Your skin shouldn't be sloughing off or red or irritated. If you are past that point and your skin is well-healed, one week would be just fine. Botox goes into the muscle, chemical peels are for superficial layers. "This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."