Thank you for reaching out to the Wefugees Community.
Holding a residence permit in Italy after being granted subidiary protection, you are allowed to travel freely within the EU for up to 90 days. Unfortunately, it is not that easy to move to another country to work and live there. If you are not underage and your situation is not a hardship case (i.e. you are the only person who is able to take care of your father being in need for daily care etc.), your options are limited to an employment residence permit. The fact that your father has a permanent residency in Germany will most probably not help with this.
Please see earlier discussed similar questions on this platform as well, including the answer given here or the information provided in this thread.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,