Stephan, if it is supposed to be fair, then it really has to be done precisely.
I think your girlfriend will not only take care of the child at home, but also run the entire household.
If it were fair, you would have to employ her with you as a full-time household employee including ancillary wage costs, i.e. social security contributions. Since she surely also works beyond the 35 hours (e.g. when the child cries at night, etc.), then overtime pay will also be added. Or directly the payment of a 24-hour household helper. Then she of course also gets vacation and weekends free or, by mutual agreement, other weekdays off or another shift arrangement that complies with the Working Hours Act.
From her salary paid by you, she would of course have to pay you a reasonable rent; possibly you also have a joint household account from which the normal, shared living expenses are paid. She would then have to contribute there as well.
THAT would be fair, because she would then also have social security.
However, this would not be advantageous for financing, because your salary must be reduced by the salary for your full-time household helper girlfriend as a constant burden. Added to this, however, is the rent your girlfriend pays you as a constant additional income.
And THEN, on this basis, the matter is fair. (although we are still ignoring the fact that she has a career interruption that is not yet compensated monetarily here)
Now you go into yourself and a quiet little room and calculate that. Even if you only assume the absolute minimum wage, you will see why so many are upset about your attitude here (rightly so!) and maybe you will consider another model. That does not necessarily have to include marriage, but it makes it easier (and one can face a separation more calmly with a well-done marriage contract).
One more thing is obviously not included in your line of thought: worst case!
You die for whatever reasons, accident, illness, crime... what else.
What then? Your girlfriend inherits nothing; if you have considered her in a will, she will have to pay hefty inheritance tax. In short: she will not be able to keep the house like that, she will not get a widow’s pension either. So you leave her quite unprotected. Also your child.
Perhaps something to think about.