I have no idea what dimensions his canvas is, or what resolution, but here's some general advice:
Draw at higher resolutions.
72 dpi is just fine for posting stuff online! But when you draw it, you want to make sure the resolution is set to higher dpi - 300 or more is good if you intend to print at some point.
Draw big, then shrink
Make yourself a nice, big canvas - when I draw my pages, I draw them at 3307x4677 pixels, 400 dpi, and when I draw illustrations, I rarely go below 2000x2500 pixels - and when you're done and it's time to save a version to post online, you can resize the canvas to something smaller. If you intend to post it on Tapastic, you can resize it to be 940 pixels across, for example. This is where you can lower the dpi to 72 if you want.
Just out of curiosity - how much do you zoom in when you draw? If you zoom in past 100%, your lineart will start looking pixellated no matter what resolution you're at.