Recent photometric observations revealed a massive, extended (MGC ≳ 105 M☉; Rh ̃ 14 pc) globular cluster (GC) in the central region (D3D ≲ 100 pc) of the low-mass (M* ̃ 5 × 106 M☉) dwarf irregular galaxy Pegasus. This massive GC offers a unique opportunity to study star cluster inspiral as a mechanism for building up nuclear star clusters, and the dark matter (DM) density profile of the host galaxy. Here, we present spectroscopic observations indicating that the GC has a systemic velocity of ∆V = 3 ± 8 km s-1 relative to the host galaxy, and an old, metal-poor stellar population. We run a suite of orbital evolution models for a variety of host potentials (cored to cusped) and find that the GC's observed tidal radius (which is ̃3 times larger than the local Jacobi radius), relaxation time, and relative velocity are consistent with it surviving inspiral from a distance of Dgal ≳ 700 pc (up to the maximum tested value of Dgal = 2000 pc). In successful trials, the GC arrives to the galaxy centre only within the last ̃1.4 ± 1 Gyr. Orbits that arrive in the centre and survive are possible in DM haloes of nearly all shapes, however to satisfy the GC's structural constraints a galaxy DM halo with mass MDM ≃ 6 ± 2 × 109 M☉, concentration c ≃ 13.7 ± 0.6, and an inner slope to the DM density profile of -0.9 ≤ γ ≤ -0.5 is preferred. The gas densities necessary for its creation and survival suggest the GC could have formed initially near the dwarf's centre, but then was quickly relocated to the outskirts where the weaker tidal field permitted an increased size and relaxation time - with the latter preserving the former during subsequent orbital decay.