Solution 1: matte floodfill
convert input.pdf -fill none -fuzz 10% -draw "matte 0,0 floodfill" output.png
Probably you'll have to adjust fuzz percentage
more details here: http://www.imagemagick.org/Usage/draw/#matte
Solution 2: color replace
I could not find a way to do it in a single command, but these two commands should work:
replace background color (taken from pixel[0,0]) with white:
convert input.pdf -fill white -draw "color 0,0 replace" temp.png
make white pixels transparent:
convert temp.png -transparent white output.png
more details here http://www.imagemagick.org/Usage/draw/#color
Tested with ImageMagick 6.6.0-1 on Windows