My dc are as bilingual as we've been able to make them!
We only speak English at home (though ds can swear in fluent weegie!)
However, they've all been educated through the medium of Gaelic since age 3. They attend the only 3-18 Gaelic school in Scotland and it's amazing watching/listening to them (now age 10, 12 and 14, just coming to the end of P6, P7 and S2) nattering away in Gaelic to teachers, friends, old ladies who we meet on our frequent trips to the Hebrides, music teachers etc.
Dd1, our eldest, is just starting exam courses and she will sit maths and history through Gaelic, as well as English, Ghaidhlig (Gaelic native speakers), French, Spanish, Art, Design&Manufacture and Physics.
All of our dc have turned out to be good at languages, maths and music (they play traditional and classical instruments) which is often seen as a benefit of bilingualism.
We regularly get weird looks (especially from family!) at our choice, and no, there's not a huge international benefit to speaking Gaelic, but bilingualism, or even fluency, in and of itself is a great thing. Our dcs school has a motto "Da Canan, Da Chultur, Iomad Cothrom" (Two Languages, Two Cultures, Many Opportunities") and I suppose that's what we're aiming for!
Go for it. I think, as long as you can communicate as well as possible with your child, then they will do well with the opportunity you are giving them.