I'm thinking about becoming a professional Wordpress Website designer and I want to know if I have to have graphic design skills in order to be a Wordpress Website designer?
Yes, you'll need them depending on the type of customer you are after. If you intend on just finding a suitable theme and tweaking it via the admin tools then you probably don't. However if you plan to actually design, and create mock ups for customer approval you will definitely need them. Plus the training will develop your perspective and appreciation of what is good design and what isn't. There are lots of good NZ design schools, and probably some some bad ones. Let us know which ones you are interested in and we can let you know how they rate.
If you want to design, you should be able to design. It is the rule in life. So, you can't except to design something in WordPress if designing is not on your skills list. WordPress is just a tool, it doesn't replace YOU. Here is my suggestion. If you aren't really suitable for designing, you should go with integration (put already designed content to WordPress) or with plugin/theme development.
If you want bespoke design you should know about the graphic design skill, also it will be plus point if you want to use wordpress theme.