We present a JWST/MRS spectrum of the quasar J1120+0641 at z = 7.0848, the first spectroscopic observation of a reionisation-era quasar in the rest-frame infrared wavelengths (0.6 < λ < 3.4μm). In the context of the mysterious fast assembly of the first supermassive black holes at z > 7, our observations enable for the first time the detection of hot torus dust, the Hα emission line, and the Paschen-series broad emission lines in a quasar at z > 7, which we compare to samples at z < 6 for signs of evolution. Hot torus dust is clearly detected as an upturn in the continuum emission at λ rest ≃ 1.3μm, leading to a black-body temperature of T dust = 1413.5 +5.7-7.4 K. Compared to similarly-luminous quasars at 0 < z < 6, the hot dust in J1120+0641 is somewhat elevated in temperature (top 1%). The temperature is more typical among 6 < z < 6.5 quasars (top 25%), leading us to postulate a weak evolution in the hot dust temperature at z > 6 (2σ significance). We measure the black hole mass of J1120+0641 based on the Hα Balmer line, MBH = 1.52 ± 0.17 · 109 M⊙ , which is in good agreement with the previous rest-UV Mg II black hole mass measurement. The black hole mass based on the Paschen-series lines is also consistent within uncertainties, indicating that no significant extinction is biasing the MBH measurement obtained from the rest-frame UV. By comparing the ratios of the Hα, Pa-α and Pa-β emission lines to predictions from a simple one-phase Cloudy model, we find that the hydrogen broad lines are consistent with originating in a common broad-line region (BLR) with density logNH /cm−3 ≥ 12, ionisation parameter −7 < log U < −4, and extinction E(B–V)≲ 0.1 mag. These BLR parameters are fully consistent with similarly-bright quasars at 0 < z < 4. Overall, we find that both J1120+0641’s hot dust torus and hydrogen BLR properties show no significant peculiarity when compared to luminous quasars down to z = 0. The quasar accretion structures must have therefore assembled very quickly, as they appear fully ‘mature’ less than 760 million years after the Big Bang.