Thank you all for the good advice!
Actually, I am not having the baby, we are having it together with my wife.
Our situation is that my wife is still working in Finland but moving here about 3 months before the birth in December. I have received the B-Permit for her. All medical inspections etc. have been done in Finland and we have the necessary documentation.
So actually we have to insure my wife first and then the baby. I have booked a time with my insurance company so I'll see what they come up with.
I will post more later this week when I hear what they recommend for the baby at this point. Interesting to see.
Pekka