I agree with your decision to switch to gnuplot. It can accomplish a wider range of actions. With the info you provided I can just try to guess that or the png drivers are missing or some variable is not correctly set.
Notes:
- Try to update to a more recent version
You are using, you know, a tool developed for *nix systems. Since the png format is a proprietary one, under Linux there are compatible library that have to be installed separately.
graphmay behave differently depending on the environment in which it is invoked.Moreover for this kind of tools can be important the environment variables under which the program runs.
We can read that, among the others, thepngfile production is specifically affected by some environment variables, for example [2]Similarly, the BITMAPSIZE environment variable affects the operation of graph -T X, graph -T png, graph -T pnm, and graph -T gif.
graph-T png and graph -T gif, which produce output in PNG and pseudo-GIF format respectively, are affected by two environment variables. If the value of the INTERLACE variable is "yes", the output file will be interlaced. Also, if the value of the TRANSPARENT_COLOR environment variable is the name of a color that appears in the output file, that color will be treated as transparent by most applications.
BTW the command you provided
echo 0 0 1 1 2 0 | graph -T png > plot.png under Linux generate the following image, that I suppose was your purpose. 
The Imagemagick [5] identify plot.png answers
plot.png PNG 570x570 570x570+0+0 8-bit PseudoClass 2c 2.1KB 0.000u 0:00.000 Tested with [graph (GNU plotutils) 2.6]