Yes, in general, if someone makes more then they pay more of the rent. It should be somewhat proportional; if you make 20% more, then you pay 20% more rent. Personally I usually try to pay for half the food/dates/household items even if I make less because we both use them equally. You could consider creating a joint account for household/child care expenses that both of you contribute to each month.

You mention you'll be able to save more under this arrangement - will your gf? Or will she end up losing money on this deal? The latter is not really fair to her, because she could perhaps save more money by choosing not to live with you and paying for half the rent. Whatever arrangement you come up with should be an improvement for both of you.

The bottom line is, you're in a partnership. What good is it to your partnership if your gf has no savings? Or does not have enough funds to enjoy herself, while you do? If you two are serious about making things work you both need to think with a team-first mentality.