  We propose to develop a cosmological model of the universe based on Weyl type
$ f(Q) $ gravity which shows the transition from decelerating in the past to
acceleration at present by considering a particular functional form of $ f(Q) $
gravity as $ f(Q) = ({H_0}^2) (\alpha_1 + \alpha_2 \hskip0.05in log ({H_0^{-2}}
Q)) $. We have solved Weyl type $ f(Q) $ gravity field equations numerically
and have obtained numerical solutions to the Hubble and deceleration
parameters, distance modulus, and apparent magnitudes of stellar objects like
SNIa Supernovae. We have also obtained numerical solutions for the Weyl vector
$ w $, non-metricity scalar $ Q $, and the Lagrangian multiplier $ \lambda $
appearing in the action of $ f(Q) $ gravity. We have compared our theoretical
solutions with the error bar plots of the Observed Hubble data set of $ 77 $
points, $ 580 $ distance modulus SNIa data set, and $ 1048 $ supernova Pantheon
data sets of apparent magnitudes. It is found that our results fit well with
the observed data set points. \bf{The model envisages a unique feature that
although the universe is filled with perfect fluid as dust whose pressure is
zero, still the weyl vector dominance f(Q) creates acceleration in it. }
