This is probably not a trivial thing. You'll either need to install a brand new circuit (assuming your breaker box has room for another) and run wire all the way from the breaker box to the outlets, or you'll need to find some nearby outlets on a different circuit that isn't as overloaded, and run wire from there to the outlets you want to switch. Either way you'll probably need to make some holes in the wall and patch them up. Also it sounds like you might not be knowledgeable about this stuff to DIY, and electricians can be pricey.
One idea: if I recall correctly, current code requires two different circuits for outlets in the kitchen. Also if I recall correctly, it requires the kitchen circuits not be shared with other rooms, so you may not be up to recent code anyway. Check whether it's possible to plug your microwave into an outlet on a different circuit.