I have produced good quality A0 maps from both ArcGIS and QGIS. Some GIS licence I have seen do limit the size of plot depending on licence but not those two and there will be pleny of other free/low cost options to explore such as Idrisi, SAGA etc. On this note you may want to consider something like Mapnik or other renderer.
It is not down to the GIS software so much as the capabilities of your printer (or whether you can outsource the printing). Bear in mind that a full colour A0 map will most likely be a very large file and so you need to consider download time on the web, given that you will want at least 300-600 dpi. At this resolution QGIS can sometimes struggle, I don't know why, so you may have to lower the resolution.
The capability of your computer to render the image and the plotter's memory limits also become a factor at this size. The standard memory which most plotters seem to come with is less than I have found adequate for quality A0 plotting even if the plotter can handle the paper size in theory. Memory is cheap though, so for a few quid, you can max out the memory of the plotter. Also, a better graphics card may help at the rendering end of things. So, on reflection, getting a good quality A0 plot is a combination of factors, the least of which is the GIS software.