This is Jason from England. I can assure you that there is least possibility that you will face any problem. Better I would suggest you to choose with organised trip and check Malta travel advisory regularly. If you are going with family you can choose HolidayRentals home. It's cheaper then hotel.
Some websites like
HolidayRentals
Homeaway
TripAdvisor
will help you to find perfect home for you and and your family in GOZO.
Very safe, I have been traveling to Malta for many years and never experienced any crime. It's a very small island and a close community. The British embassy states on their travel website in Malta ... "Crime against tourists is rare" The U.S. department of state website says "No indigenous terrorist or extremist groups are known to be active in Malta and no foreign terrorist organization has carried out an attack against U.S. interests in Malta in recent years."
The only issue we had on Gozo was taxi drivers trying to rip us off and overcharge us. It seemed very safe to me, it's very quiet and sleepy
FFS, everywhere in Europe is far far safer than the USA. Gozo is a tiny island. Just go.
