The Verdict: Not eligible
Your passport is not covered by a German working holiday programme, so this route is closed. Look at the Opportunity Card instead, which lets you come to Germany for up to a year to look for work.
Germany has programmes with Argentina, Australia, Brazil, Chile, Hong Kong, Israel, Japan, the Republic of Korea, New Zealand, Taiwan and Uruguay, and a separate agreement with Canada. They are treaties, so nothing but the passport qualifies you.
The Opportunity Card is open to any nationality but needs a recognised degree or vocational qualification. The EU Blue Card and the skilled worker permit need a job offer. The Germany Skilled Migration quiz covers all three.
If a parent or grandparent was German, take the Citizenship by Descent quiz: a citizenship claim would make a permit unnecessary.