If you use the correct "Center Waste Kit" you will have plenty of room.

You need to get a "Disposal type Center Waste Kit"

In a Disposal type center waste kit you will get the "center baffled tee" and one cross tube that has a 90deg bend on the end to connect to the sink tailpiece opposite of the disposal. The second cross tube does not have a bend on the end. It is a straight tube that has a flat flange on the end of the tube.

The plastic elbow that comes supplied with the disposal is discarded. You then put the rubber gasket in the disposal port, then hold the flat flange on the cross tube against the rubber gasket and slide the metal bracket on the tube and bolt it to the disposal body as indicated in your disposal instructions. That will leave you a discharge line from the disposal that is horizontal at the disposals discharge port height. The discharge line from the center baffled tee will then fit into your trap without lowering the trap.

You can find the "Disposal Type center waste kits" at any hardware or home supply store where they sell the drain parts. They will be approximately the same price as the standard double sink center waste kits (about $12)