H-4 child of a domiciled H-1B parent Yes — by published rule
Domicile-based post-SB 1528: an 'Eligible Nonimmigrant' holds a visa permitting domicile — operational chart: A, E, G, H-1B, H-4, I, K, L, N, NATO, O-1, O-3, R, T, TPS, U, V (plus I-485-filed, refugees, asylees). F-1/F-2, J, TN/TD, B, C, D, H-2/3, M, P, Q cannot domicile.