Hi tskalex,
The following is just pure personal experience, not immigration advice.
It is like JandM said. A Skilled Migrant visa is as the name applies about "skills". If you hold work experience within Germany (which is a comparable labour market to NZ), a degree which will be assessed by NZQA as recognised/comparable here in NZ, being under 30 years of age, and having a skilled job offer related to your degree, your chances might be pretty good.
I did the same when I came here you. Arrived on a Working Holiday Visa right after graduating, accepted a job - my employer needed to give me a fixed contract (expiring when my WH visa expired). Then could gave me a full time permanent offer which we used to fill out the EOI. After submission of the ITA, I was able to get an Essential Skill Work Visa as my Residence Visa is pending.
I can tell you from experience that Kiwis want to see you in person for an interview. No one responded to my applications from overseas.
Good luck on you mate
Btw, it is all together a pretty long and expensive journey from Working Holiday Visa to Residence. I submitted my application in July 2016 and still waiting. Residence is not a "nice to have", you have to commit to this country and put your heart into it