Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to achieve in practice. However, it is known that LLL states appear among the excited states of weakly interacting gases even in a nonrotating trap, by working at fixed finite angular momentum. Thus, even in the absence of rotations or for moderate rotation frequencies, Fractional Quantum Hall (FQH) states can be accessed as excited states at finite angular momentum. Motivated by this, and by recent experimentally demonstrated excitation protocols for two particles, we show that such states can be selectively addressed at larger particle number, and we propose imaging techniques to resolve their distinct microscopic structure. In particular, we suggest that recently developed excitation and imaging techniques for rotating few-fermion systems allow for a detailed experimental investigation of FQH wave functions and to study the crossover to large particle number. We illustrate the evolution of the excitation spectrum with rotations at weak interactions for $N=6$ spin-balanced fermions and show how sampling of the few-body wave function allows to discriminate between total guiding center, center-of-mass vortex, and hyperradial excitations, respectively, thus providing detailed and versatile probes of the microscopic structure of FQH states.