Hey Bronsay, welcome to the Boardworld Community!
What sized boots do you wear? Where do you plan on riding mainly? Australia, overseas, or both?
Firstly, don't worry too much about where the board comes up to in regards to your height. The most important factor is your weight; the board has no idea how tall you are, just how much force you exert, which is determined by your weight.
Every snowboarder can comfortably ride a range of board sizes. Boards on the smaller end of the scale will have advantages, i.e. more maneuverable, easier to spin, easier to press, easier to jib, and they are generally more fun to play around on - although they are less stable at speeds, not as good for carving, and don't float very well in powder (although other factors effect that too). Boards on the larger end of the scale are more stable, carve better, and float better in powder - although they aren't as maneuverable or as fun to jib around on.
The advice I always give people looking to buy one board, especially those who are just starting out and exploring their style, is to buy something which is going to be
versatile. You want a board which can ride well in a variety of conditions so you can have fun regardless of what type of riding you decide to do on the day. Buy a versatile board in regards to shape and flex, but most importantly a versatile size. If you buy a board which can comfortably ride everything from park to deep powder, then you have a board which will last for a long time while you explore different terrain, different conditions, and the different aspects of snowboarding.
In my opinion, yes your snowboard is certainly on the short size for your weight. As mentioned this will have clear advantages and disadvantages. You have to ask yourself what type of riding you think you will doing more of? If you want to get into the park and really progress in regards to freestyle, then your board choice should be fine. However it's not ideal for freeriding (riding the mountain, speeds, carving, powder etc...).
If you can get back to me with further information about your intentions, we will be able to help you better. Please let me know if you have any questions.
Also please have a read of these two articles:
Snowboard Characteristics
Snowboard Selection