  We detail a new fast radio burst (FRB) survey with the Molonglo Radio
Telescope, in which six FRBs were detected between June 2017 and December 2018.
By using a real-time FRB detection system, we captured raw voltages for five of
the six events, which allowed for coherent dedispersion and very high time
resolution (10.24 $\mu$s) studies of the bursts. Five of the FRBs show temporal
broadening consistent with interstellar and/or intergalactic scattering, with
scattering timescales ranging from 0.16 to 29.1 ms. One burst, FRB181017, shows
remarkable temporal structure, with 3 peaks each separated by 1 ms. We searched
for phase-coherence between the leading and trailing peaks and found none,
ruling out lensing scenarios. Based on this survey, we calculate an all-sky
rate at 843 MHz of $98^{+59}_{-39}$ events sky$^{-1}$ day$^{-1}$ to a fluence
limit of 8 Jy-ms: a factor of 7 below the rates estimated from the Parkes and
ASKAP telescopes at 1.4 GHz assuming the ASKAP-derived spectral index
$\alpha=-1.6$ ($F_{\nu}\propto\nu^{\alpha}$). Our results suggest that FRB
spectra may turn over below 1 GHz. Optical, radio and X-ray followup has been
made for most of the reported bursts, with no associated transients found. No
repeat bursts were found in the survey.
