  Two distinct scenarios for the origin of the ~ 4 \times 10^8 M\odot of dust
observed in the high-redshift (z = 6.4) quasar J1148+5251 have been proposed.
The first assumes that this galaxy is much younger than the age of the universe
at that epoch so that only supernovae (SNe) could have produced this dust. The
second scenario assumes a significantly older galactic age, so that the dust
could have formed in lower-mass asymptotic giant branch (AGB) stars. Presenting
new integral solutions for the chemical evolution of metals and dust in
galaxies, we offer a critical evaluation of these two scenarios, and
observational consequences that can discriminate between the two. We show that
AGB stars can produce the inferred mass of dust in this object, however, the
final mass of surviving dust depends on the galaxy's star formation history
(SFH). In general supernovae cannot produce the observed amount of dust unless
the average SN event creates over ~ 1 M\odot of dust in its ejecta. However,
special SFHs can be constructed in which SNe can produce the inferred dust mass
with a reasonable average dust yield of ~ 0.15 M\odot. The two scenarios
propose different origins for the galaxy's spectral energy distribution,
different star formation efficiencies and stellar masses, and consequently
different comoving number densities of J1148+5251-type hyperluminous infrared
(IR) objects. The detection of diagnostic mid-IR fine structure lines, and more
complete surveys determining the comoving number density of these objects can
discriminate between the two scenarios.
