Personal property would be your tank, equipment (lights, filters, pumps, etc) for COVERED PERILS. I put this in bold because if you read that section of your policy these are the types of incidents that will be covered.
As for any live stock such as fish, corals, inverts will not be covered (they are not considered personal property to an insurance company: Check Coverage C on your policy). Pet insurance is different than what us hobbyist are thinking about "aquarium insurance" such as a major tank crash (power outage for example) and our inhabitants are not covered. Pet insurance is geared toward vet bills which mimics human health insurance. Such as your dog breaks their leg and needs surgery.
Local fish stores and aquaculture facilities can get business insurance that does indeed cover their livestock since it is for business purposes.
Nearly every hobbyist would have either a HO3, HO4 or a HO6 which is homeowners insurance, renters insurance or condo insurance. Most insurance companies don't deviate from those insurance policies. None of which cover livestock or living animals of any kind (occasionally/rarely dog or cat may be insured for simple things). You would need a rider or an inland marine policy specifically designed to insure your live stock. If happen to find a willing agent, you would need to keep all receipts of every coral and fish purchased or have a coral expert appraise the coral/fish for value purposes. That's if and only if you can find an insurance agent willing to write one. Even at that point the agent would have to get approval from their underwriters to see if their company would even want to take on that risk. Most common answer from the underwriter is No.
From time to time you will find an home insurance company dedicated to very wealthy individuals whose policy covers pretty much everything and anything. Let's just say those who have these types of home insurance policies tend to live in homes well over a million dollars.
I've seen people who swore up and down that their local home insurance policy will cover their tank inhabitants. Their agent said sure "of course". When the time comes an adjuster comes out and does not cover a single fish or coral. Also there have been times when the customer had a written rider printed by the agent. The agent simply files the incident under aquarium leaving out details of "live stock" to get around the underwriters so they don't get caught. But that puts the customer and the agent at risk of having the claim denied or set up for immediate cancellation because of improper insurance.
In the end if you find an agent willing to write you an aquarium policy make sure everything is in writing that specifically explains your livestock, fish and corals are insured for covered perils and any other agreed upon incidents. Hope this helps.