That is where the flying Barracks comes in handy. You can fly a Barracks over and build enough Marines to fight off or delay the Mutalisks if you are very quick and not spotted. You need to secure at least one extra island with Gas for Battlecruisers. Using your initial Minerals and two Gas mines, you should be able to build enough Battlecruisers, if you conserve your Gas, to take out the Zerg. The next concern is Guardians.
Guardians can take out any island defenses from a distance.
Battlecruisers are the answer here also. You can get Battlecruisers around the same time that the enemy gets a group of Guardians if you start fairly early, use at least two Starports, and conserve Gas. Use the Science Vessel's Irradiate on collections of Guardians, Mutalisks and Hydralisks. This works very well. The Zerg can use the Queen's Broodling spell to get rid of Siege Tanks and Goliaths, so you might want to skip using these against the Zerg, or keep them behind Missile Towers.