I’m not an expert but as far as I’m aware the marriage vows state clearly that you will accept children lovingly from God. Preventing the conception and birth of children is definitely forbidden, ie using artificial contraception or abortion. However, natural family planning (eg rhythm method - at least that’s what we used to call it) is allowed and that involves abstaining from sex for certain days of the woman’s cycle. So at least some abstinence within marriage is allowable.
However, I don’t think deliberately avoiding sex entirely is a fulfillment of the sacrament. If for some reason sex isn’t possible or would be highly dangerous medically, that’s one thing. But choosing not to in order to avoid having children isn’t.
As far as avoiding sex for spiritual reasons within a marriage, I’m thinking of the parents of St Theresa of Lisieux who, according to St Theresa’s autobiography were very devout and wanted to have the sort of marriage you describe for reasons of chastity and holiness. But were told by their priest it wasn’t acceptable and they should try to have a family.
I know you say in this (presumably hypothetical) scenario you love the girl and you want to be together, but I can’t help wondering what would be the purpose of such a marriage other than convenience for legal, practical and public appearance purposes. To me - and I’m sure someone here will shoot me down in flames for saying it - that isn’t a real marriage and the vocation element would lie elsewhere in your lives. Other than the legal benefits, why bother with such a sacred vow and life long unbreakable commitment? You can still work together as platonic friends and partners in the service of God without the sacrament of marriage if you are serious about sex not being be part of your relationship.
But that’s just my view and I’m sure there are lots of way more clued up and intellectual people here who can quote chapter and verse of Canon Law who will set you straight. I’d be interested to know if I’m completely wrong about it.
Good luck with everything and whatever road the Lord calls you to take.
xx