Do you have to have (or does it help) to have a garbage disposal with a dish washer?
Dishwashers usually have a built in food disposer, so having one is not required. 

I also suggest just replacing the existing disposer instead of removing it altogether. Cheapest ones cost around $60 and since they usually feature a quick change mechanism, the whole process takes 15 minutes. But if you remove one, then you will have to reroute a drain pipe to accommodate for the missing disposer. Really not fun to do in the cramped space under the sink.