It says this about Graphic Designer on the INZ skill checker.
http://skillshortages.immigration.go...phic-designer/
Requirements to claim points for skilled employment (Category A)
A relevant recognised qualification which is at, or above, the qualification level on the New Zealand Qualifications Framework. The qualification must correspond to the skill level indicated for that occupation in the Australian New Zealand Standard Classification of Occupations (ANZSCO)
OR
The relevant work experience that the ANZSCO indicates may substitute the required qualification
OR
The relevant requirements specified in the Long Term Skill Shortage List (LTSSL) for your occupation (if your occupation is included in the LTSSL)
OR
Five years of relevant work experience.
It appears that you wouldn't make the grade, not having either the relevant recognised qualification, or the work experience which they would accept as substituting for it.
The best place to look for the detailed regulations about claiming points on the EOI is here.
http://www.immigration.govt.nz/opsmanual/6954.htm SM6 has a chart of all heading under which points can be claimed, and the last column shows which other section to look in for the requirements.