What should I consider when replacing an outlet serving two kitchen circuits?
A GFCI is a good idea because of the location of the outlet.  However, I don't think that a GFCI that can simultaneously protect two circuits even exists (and I doubt one would fit into a single-gang box if it did exist), so I believe you have a couple of options:


Install GFCI breakers on the dishwasher and disposal circuits, and use a regular outlet under your sink with the tab between the screw terminals broken off.  This may be what you already have; the breakers will have a Test button on them if so.  If the supply for the disposal runs to the switch first then to the outlet, this is the only way that the switch will be covered by the GFCI.  In your place, this is what I would do: safer and less work, albeit a little more expensive.
Use GFCI outlets.  As I said above, you'd need two GFCIs to protect your two circuits, so you would have to install a double-gang box in place of the existing gang-box or add another single gang box then run the wiring for one of the appliances to it instead (in your place, I'd do the latter and use a remodeling box for the new outlet).  However, this means that the switch for the disposal wouldn't be covered by the GFCI, potentially risking an electric shock.