Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field (“fuzzy”) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have “solitonic” cores of radius ~ [italic lambda] [subscript deB], surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, [italic lambda] [subscript SI], with [italic lambda] [subscript SI] > [italic lambda] [subscript deB] --called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-[italic lambda] [subscript deB] limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, P [subscript SI] [is proportional to] p². We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of R [subscript TF], the radius of an SI-pressure-supported (n = 1)- polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [“too-big-to-fail” + “cusp-core”]-test if R [subscript TF] [is greater than about] 1 kpc