Hair texture is polygenic — many genes contribute, with no single dominant rule. Here’s a probability across the texture spectrum based on what each parent has.
Hair morphology in Europeans is roughly 45% straight, 40% wavy, 15% curly (Medland et al. 2009). The strongest single known variant sits in trichohyalin (TCHH), expressed in the developing inner root sheath of the hair follicle — but it explains only about 6% of variance. The rest is polygenic, with at least a dozen smaller-effect loci identified, plus EDAR variants in East Asian populations that produce a different straight-hair phenotype.
Hair texture also genuinely changes with age. Many curly-haired adults had stick-straight baby hair (and vice versa) — the curl gene programs the shape of the follicle, which keeps maturing through childhood. Hormones during puberty can shift texture again. The hair you'll see at age 5 is a much better predictor than the hair at month 5.
Source: Medland SE et al. Am J Hum Genet 85:750–5 (2009), "Common variants in the trichohyalin gene are associated with straight hair in Europeans."