No, that's actually a system admin's job.
I do design too, but it's a minor part of what I do, basically because **anyone** can do that, and most people are, for free. After they get into trouble . . that's when they come to me.
No most of my job is developing custom websites for customer applications. What I do is make sites that actually **do** something for the customer. I have about ten or twelve that are shopping-cart sites, the customer can go in add, edit, remove products, collect orders, it uploads pics and auto-sizes them bla bla . . another is a subscription site, the guy has a stocks newsletter (except he really DOES have good stocks info

) and he makes about 4K a month on it . . . 6 or 8 membership-based real estate sites including image uploads and whatnot . . . a few message boards . . . a lot of secure connection interface stuff . . . and lately an online writing lab for a college that won a national award. Of course, my name wasn't mentioned, I'm just one of the slaves that built the pyramid. But it was pretty cool anyway.
I write the programs that do all that stuff. From scratch. Hand coded.
If you want to get into web design? I've been doing it for about 8 years now. Here's the "real world view:"
It's a bitch.
Every day, someone's viewing your source code, looking for a chink in your armor, anything they can find to call up your boss and tell them why you're an idiot. You spend half your time trying to fend off everyone who seems to think your job is cool, and the other half keeping up with the technology. People don't want to pay you, but they want to call you up and suck up your time asking you stupid questions they're too lazy to figure out themselves so that they can do the job **without** paying you. You waste a lot of time dealing with customer issues that have nothing to do with you, for example, explaining to someone how the website you designed for them last week as nothing to do with why they are too stupid to get their email because they can't remember their password. Customers call up your boss and try to get you fired because you didn't drop everything RIGHT NOW to change the email address on their site, and the only reason they need THAT done is because they keep getting spammed from all the porn sites they visit.
Then there's the work. Hours and hours poring over your code, getting it all to work together, making it easy to understand for the visitor, to come up with a system that WORKS. The hard part is that 90% of your programming is spent writing error traps and figuring out all the possible ways a user can push the wrong button, refresh the wrong page, enter the wrong value into a form, or actually TRY to hack you just for no other purpose than to f**k up your day.
But if you come out the other side and it works, you throw all your best hack friends at it and they can't break it, it's worth it. My wife thinks I'm insane. She's prolly right. But you have to be passionate about what you do, or you doing the wrong thing.
If you **do** decide to get into web design - never ever EVER make the assumption that most "designers" do. They put together a pretty web template and let the "programmers" figure it out. This is VERY VERY BAD. Get an understanding of the tools behind your "skin" and design accordingly: FORM FOLLOWS FUNCTION.

Never forget it.