We present the results of a search for astrophysical sources of brief transient neutrino emission using IceCube and DeepCore data acquired between 2012 May 15 and 2013 April 30. While the search methods employed in this analysis are similar to those used in previous IceCube point source searches, the data set being examined consists of a sample of predominantly sub-TeV muon-neutrinos from the Northern Sky (-5 degrees < delta < 90 degrees) obtained through a novel event selection method. This search represents a first attempt by IceCube to identify astrophysical neutrino sources in this relatively unexplored energy range. The reconstructed direction and time of arrival of neutrino events are used to search for any significant self-correlation in the data set. The data revealed no significant source of transient neutrino emission. This result has been used to construct limits at timescales ranging from roughly 1 s to 10 days for generic soft-spectra transients. We also present limits on a specific model of neutrino emission from soft jets in core-collapse supernovae.