First off: no, your carrier does nothing to protect you from malware. It's entirely up to you. But you have a tool to help you keep your phone safe: Android's permission model. When you install an app on your Android phone, it tells you before you install it what it can do to and with your phone. It's up to you to decide whether you trust the app with that ability.
For example, you might go on Google Play and download a game that looks a little like Angry Birds, but it wants permission to directly call numbers. If you install it anyway, you may be surprised a month later to see it has been repeatedly calling premium-rate numbers behind your back, costing you hundreds of pounds. Even an app that wants internet access and the ability to read your SD card might be looking for your 'private' photos so that its owner can sell them on the internet: or if it wants to "take photos and videos", it might use that to take its own when you least expect.
The threat posed by malware on Android is completely different to on PC. "Damaging" your storage is not an issue, but there are more harmful things that malware can do, to invade your privacy, steal your money, or attack your friends and other contacts.
The question is trust, in two ways. You have to decide whether to trust each app you install with the permissions it asks for. Whether you need an anti-virus is down to whether you trust yourself (and everyone else who uses your phone or tablet) to make that decision.
If you're the kind of person who clicks on emails that claim to be from your bank, or on those banner ads that offer you a free download to speed up your internet connection, then you need an anti-virus. If you're the kind of person who doesn't even download an app from a reputable source without checking out reviews on independent sites, then it's probably not necessary.
Before you decide, bear in mind that most anti-virus products also offer browsing protection: they try to detect phishing sites and other harmful websites. App downloads aren't the only source of malware. And if a vulnerability is discovered, which would allow apps to bypass the permission system (such as the
/dev/exynos_mem bug in the samsung-galaxy-s-3), they'll even protect you from malware that exploits that bug.