I assume from the question that you are on city water, without a well?
We have used a berkey for going on 6 years to filter both city water and now well water. They provide terrific filtration, albeit at a price. However, with 4 adults and 4 dogs you are going to want a lot more than 8 gallons a day, for anything other than bare survival. Probably double or triple that, or more.
All that said, there is no replacement for stored water. Rivers can become contaminated. A berkey may filter out bacteria and viruses, and some chemicals, but there's no limit to what could wind up in that water during a hurricane or similar disaster. Would you have wanted to filter and drink the flood waters in NOLA after Katrina? Also depending on the severity of the situation, travel may be difficult or impossible. Or unadvisable. Would be far easier to have a large quantity of water stored ahead of time.
Are you in a location that allows rainwater collection? Any homeowners or other restrictions on storage tanks?