shp2pgsql is indeed a command line tool. It comes with your PostgreSQL/PostGIS installation (usually) and, if not accessible via PATH-variable, can (usually) be run from within the /bin-folder in your PostgreSQL-Installation. You can also always 'make' the programm from source in any location yourself, if needed.
EDIT:
One way to set up a script (independent of whether you use it within qgis own python environment or not) would be to use Pythons subprocess (or os.system) module (check related question here) to write to shell and execute shp2pgsql.
A slightly more sophisitcated solution to (batch) insert (multiple) shapefiles via script could be to implement ogr2ogr via gdal/ogr module within python (check this blog). That, however, would require a working installation of the gdal core library, and the respective Python bindings (at least to use outside of QGIS Python environment, where it is pre-installed AFAIK), which can be tiresome at times. Once installed correctly, it offers a powerful (I dare say almighty) toolset for geodata management and manipulation via Python, though.
Apart from that, the blog link I provided also states the implementation of a batch insert script/tool (which operates ogr2ogr) in qgis 2.8 toolbox...maybe that can help you, either with your work directly or (via sourcecode) to point you in the direction of creating your own tool.