This is a common issue when adding or changing a disposal. It is no problem to drop the p-trap -- the real issue is that the drain line coming out of the disposal and into the p-trap must be higher than the drain line that exits the p-trap and goes into the wall or floor. Otherwise the water will not drain from your disposal and your disposal will die young and with a voided warranty. Not to mention that your sink and dishwasher may not drain properly.
Your disposal installation instructions (and local plumbing code) will tell you about the specs for the drain lines.
If the existing drain line is too high for your disposal, you will have to lower your existing drain line, and probably knock a hole or two in your walls.