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 Schrodinger-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 $simlambda_text{deB}$, 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, $lambda_text{SI}$, with $lambda_text{SI}> lambda_text{deB}$ -- 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-$lambda_text{deB}$ limit, however, we can model all three by fluid conservation equations for a compressible, $gamma=5/3$ ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, $P_text{SI}propto rho^2$. 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 $R_text{TF}$, 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 $R_text{TF}gtrsim 1$ kpc.