Home Improvement Questions? Ask a Handyman for Answers
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Based on your description I don't see the need to replace the carpet but if it soaked up enough water to bring down the plaster the carpet and pad should be lifted and dried out. Sometimes than can be done while leaving the carpet in place sometimes not.
No need to demo anything other than removing the wet plaster and drying out the ceiling. If this is plaster and lathe them removing all the ceiling plaster (just the plaster not the lathes) can make installing new sheet rock on the ceiling easier.