I'm assuming that the figures for your lens are '35mm equivalents', rather the true focal lengths, as that's fairly standard when describing the lenses on digital SLRs.
A cheapo fixed-focus camera typically has a lens of around 50mm. (Indeed that was the standard for many years, although more recent cameras often have lenses of around 40 to 45mm). So your current zoom lens does what a 'bog standard' lens would do, plus it's got quite a good 'wide angle' facility (down to 18mm) but almost no 'telephoto' capabilities whatsoever.
Studio photographers usually like to have lenses with focal lengths of no less than 80mm. (Filling the frame with someone's head with a 50mm lens results in distortion, making their nose look bigger than it should be. You need a lens where you can fill the frame with someone's head from further back). In the days of fixed-focus lenses (for conventional SLRs) most people would probably have opted for a 135mm lens for studio photography.
With your criteria you'd probably find that a lens covering something like 80mm to 150mm (or, at the most, 200mm) would meet most of your needs. Longer lenses are expensive, unwieldy and (unless you're into things like sports photography) probably unnecessary.
Chris