Most adults globally are lactose intolerant — this is the human default. Whether your child can drink milk into adulthood is mostly determined by ancestry.
Lactase persistence — the ability to digest milk into adulthood — is the genetic mutation, not the other way around. Mammals are programmed to stop making the lactase enzyme after weaning; humans who can drink milk as adults carry a regulatory variant near the LCT gene that keeps the enzyme on. The canonical variant in Europeans is LCT −13,910*T (Enattah et al. 2002, Nat Genet).
Lactase persistence evolved independently at least four times in the last ~10,000 years — in Northern Europeans, in East African pastoralists (Tishkoff et al. 2007 identified three additional African variants), and in some Middle Eastern populations. That's why ancestry is the strongest single predictor: ~95% of Northern Europeans are persistent, vs. ~10% of East Asians and ~25% of West Africans.
The "intolerance" label can be misleading. Most non-persistent adults can still handle small amounts of lactose (a glass of milk with food, yogurt, hard cheese) without major symptoms. And your kid will be fine either way — we have great alternatives now.
Sources: Enattah NS et al. Nat Genet 30:233–7 (2002), "Identification of a variant associated with adult-type hypolactasia"; Tishkoff SA et al. Nat Genet 39:31–40 (2007), "Convergent adaptation of human lactase persistence in Africa and Europe."