Will home insurance cover dog damage in home?

Yes. I used to work for an Insurance company in the claims department. It will be covered under the section "personal property" of your Homeowners policy. You will however have to pay your deductible. If the deductible exceeds the amount to replace the item, the company will not pay. If it costs more then your deductible to replace it, then the company should issue a check for the remaining amount. So if it costs $2000 and you have a $500 deductible, you should get $1500.