I recommend the Canon 50mm f/1.8 STM. On a crop body, it will become equivalent to somewhere around 85mm, which is perfect for portraits. It's dirt cheap and the same price as the old nifty-fifty, or even less if you snag it refurbished. The build quality is a HUGE step up from the old Mk ii version and optically is the same - which is good. The 50mm f/1.8 ii was known to have really good sharpness stopped down and really wide aperture for the price. The new version has an STM motor, which is okay, nothing great, but much nicer than the micro motor of its predecessor, and 7 rounded blades which will develop some nice out-of-focus details.
I usually interpret my copy's max aperture as f/2.8. I don't have to go much wider very often and the sharpness really improves from f/1.8 by f/2.8.
You can still choose to shot at f/1.8 and get sharp images, as long as you feel like spending a little time in post sharpening them. Be careful that you understand how shallow the depth of field becomes at f/1.8 however - sharpening won't be enough to bring most out of focus areas into acceptable, let alone, sharp focus.
Acting as an ~85mm lens on your camera, at f/2.8, the subject isolation you will be able to achieve will still be pretty comparable to anything at f/1.8 (unless you are up in your subject's nose) and the sharpness will definitely be worth it.
To answer you original question, the nifty-fifty is way sharper than the 18-55mm at almost all apertures. I have previously owned the 18-55mm II and STM, and neither were any sharper than just "decent". The 50mm 1.8 stopped down between f/4 and f/8 is pretty comparable to much more expensive high end lenses - and your 18-55mm can only obtain a max aperture of 3.5 - 5.6 (depending on focal length) anyway.
Link:
Canon EF 50mm f/1.8 STM Refurbished Lens ($90 at current writing)
It's out of stock now, but watch closely, as I have seen it jump back into stock pretty quickly before.
If you decide to go this route, you could sell your 18-55mm in to
KEH Camera or
B&H for a decent enough price to almost cover the cost of the upgrade entirely.