Absolutely. You will find many proponents of a single bowl kitchen sink and there is no problem installing a garbage disposal with them.

I don't think youll be able to fit a trashcan on the same side as the garbage disposal. On the other side, it should fit. With that said, I would advise against getting the drawer pullout for the trash for two reasons. One being, if there is a leak, big or small, your access to plumbing is limited unless you take out the entire pullout. And keep in mind where your plumbing is coming in from. Our water supplies were from the floor and out drain was through the wall. The water supply would have hit the back of the pullout. The sink cabinet is our only cabinet that we used doors for. We have drawers/pullouts for every other base cabinet in the kitchen. Two, it is my personal opinion that the workflow is off balance with the sink and garbage being in one cabinet. Generally if two people are in the kitchen, one will be by the sink (prepping, cleaning, etc), so access to the garbage for the other person is limited, unless the first person moves over. But, if space is tight and you can't find anywhere else to put a trash pullout, 'you gotta do what you gotta do!' We ended up using a 12 inch base cabinet with the wire pullout and moving the wire racks all the way down and putting an IKEA trash can with lid inside. Works well and takes up very little space. (also, I can't tell you how much we love our Domsjo sink and Wasteking!) Good luck!

My large disposal for my farmhouse style sink connects up to a 1-1/4" drain line and works just fine. I think the main issue for the OP is whether there is any problem with the disposal's mounting bracket in relation to the drain hole of the smaller sink. These brackets can sometimes be a pain even with a normal-sized sink.

M Miller - Why did't I contact WasteKing? Honestly it never occurred to me. The garbage disposal had consistent issues with certain classes of waste. It chewed through anything hard and solid. That is where the power of the motor comes into play. The design of a garbage disposal is muck more than simply the motor. Just like a car and pretty much every other product. You can chose to believe me or not. Really does not matter to me. I am simply relating my experience with the 1hp Wasteking, Legend Series I got from Costco. My previous Insinkerator had its issue with raw chicken skin. I did not think to call and complain about that either. It was just a matter of using the correct tool for the job. I am glad that Wasteking works well for you. For me it did not. I was much happier with the Insinkerator and felt it was worth the additional cost. Not everyone will agree with me. That is fine. Competition is great for any industry so I am happy there are other options out there. aliceinwonderland_id - I have to disagree with you on the landfill. With the way Garbage is compacted many landfills have an issue with getting enough oxygen down to the organic waste to decompose it. If you run enough water in your disposal it will flush the waste all the way to the main pipes where additional water flow will keep it moving. At least that is my theory :) More and more cities are setup to handle the "solid" waste and make use of it. Not that I don't believe you but would you point me to a link discussing the issues with Garbage Disposals and pipes/Ph, etc?