What is the name of your state (only U.S. law)? NC
... the cost might be around $2500. ... they wanted to replace the carpet and charge me asap. I wondered if I'm legally obligated to pay for the carpet of the entire apartment or just the damaged part.
Updates:
If I have to pay for the whole piece of carpet...
1. Since I just moved in, could I request to replace the carpet till the ending of my leasing term? Thus, I may be able to avoid any damages during my term.
2. Could I request the receipt of the new carpet?
...
In reading through your thread, smiledays, I noticed that no one addressed your question number two - and it is an important question.
Not only CAN you request of your landlord a copy of the receipt for the cost of the new carpet, you SHOULD request a copy of the receipt. The landlord should provide it to you as a matter of course, and the landlord should be able to justify the charge by letting you know how old the original carpet was when you moved in.
Also, you not only CAN request a delay in replacement of the carpet, you probably SHOULD request a delay in the replacement of the carpet - because with a puppy, more damage to the carpet is likely, this no matter what steps you take and how careful you are in trying to prevent additional damage. You do not want to be held responsible for a SECOND $2500 carpet at the end of your lease.
I don't know about the other contributors to this thread but my "sage" advice comes from having a puppy that was NOT crated when left alone. We left her in an "indestructible" area of the house and when we returned a short time later, the puppy had pulled up tiled flooring and chewed it, and had eaten a hole in the wall. It was only in retrospect that we learned crating is smart (and far less costly).
As a note, I like FarmerJ's suggestion about trying to negotiate a payment plan with your landlord, if the landlord insists on having you cover the costs of a new carpet now. If you are being charged a monthly pet fee, this monthly pet fee should be going toward any pet damage, too.