Well, they do two different things. A kitchen designer should help you with a layout and choosing finishes. A GC should supervise all of the work, including hiring subcontractors and arranging their schedules.

If you plan to use ikea cabinets and are happy with your existing layout, you may not need a kitchen designer. But I would suggest posting your current layout here to see what suggestions you get. If you are going to all the trouble of remodeling, you should defintiely make sure you are maximizing your space.

You may also wish to talk to a couple of kitchen designers to see what they have to offer you. Depending on your layout and door style, you may find that ikea isn't the best or even the cheapest option--especially since you are not planning to diy and will need to pay someone to assemble and install your cabinets. (Although we did just that in our last kitchen and felt that we got an excellent value despite paying for labor, but ymmv)

If you are keeping your existing layout (no plumbing or electrical changes) and using IKEA cabinets, you may not need a KD or a GC, just a cabinet installer.

Why don't you draw up a diagram of your current space and your specific ideas and post them here for feedback? Include measurements. This New to Kitchens discussion will give you a lot of good tips for what information is needed to give you the best advice

Use a Design+Build kitchen firm, if there is one in the area. A D+B firms takes care of the design and then the construction. If you use a designer, you have to pay for the design. If you use a D+B firm, the design charges are usually rebated if you then build the kitchen with the firm.