What you're trying to accomplish by hand, it's pretty much what ArrayList does for you - use that class, instead.
Under the hood, ArrayList uses an Object[] for storing items, under a certain capacity constraint. When the array is filled (as new items are added), a new array with doubled size is created and all the items in the original array are copied in it. All this happens automatically, and it's transparent for the programmer.
Given that in the sample code you're storing an array of objects (Strings), there'll be little difference in performance if you use an ArrayList for storing them, so there's no real reason to reinvent the wheel!
