# returns: PyQt4.QtCore.QString(u'EPSG:26913')
qgis.utils.iface.activeLayer() returns a reference to the active QgsMapLayer.
QgsMapLayer.crs() returns the crs or QgsCoordinateReferenceSystem for the layer.
QgsCoordinateReferenceSystem.authid() returns the Authority identifier for the crs as a QString.
However, this is assuming there is an active layer, it is of a vector type, and it has a valid crs. You will want to test for validity of those items before committing to reprojecting a raster.
If you are reprojecting, using GDAL.Dataset.SetProjection() will not suffice, since it will only assign a projection and not reproject (warp) the raster to the same as your vector layer.