Doing development on an iPad is definitely possible, but how well it works for you will depend a lot on your workflow. In particular, you may run into trouble when it comes to debugging, especially if you need a good JavaScript debugger.
Debugging
As an experiment I recently tried some editing of a (mostly JavaScript) webapp I've been working on using my iPad. The editing went relatively smoothly (I used Textastic), but debugging the JavaScript was a pain. As far as I'm aware, the only thing that comes close to a proper debugging tool on iOS is Firebug Lite, which has some substantial limitations. Because it's not integrated into the browser, it can't catch a lot of problems. No syntax error catching (you're left hunting for that missing bracket on your own), and no reporting of HTTP issues if an external script isn't loading properly.
The interface is also pretty rough to use on a touch device — small tap targets, and it resizes strangely if you try to zoom. As someone who relies a fair bit on Safari and Chrome's developer tools when doing JavaScript development, I found it fairly frustrating when I ran into any sort of bug.
That said, if your development is more server-side, or you otherwise don't depend on those sorts of debugging tools, the iPad could very well make a good development environment for you.
Editor Options
If you just want to use Vim, then an SSH client like Prompt or iSSH would work well, combined with a remote server somewhere (which you'll need anywhere for viewing files). If you want an option that doesn't require network access, there is an iOS port of Vim, but it's worth noting that the files are only accessible through iTunes (i.e. you can't upload them to an SFTP server or view them locally with Safari).
If you want a more native experience, Diet Coda is worth a look, as it integrates a lot of useful tools — SFTP, a full SSH client, code editor and browser. It's definitely on the pricier side of iOS apps, but I've read good things about it.
Textastic is another good editor, with some nice extensions to the software keyboard (useful for making changes in a pinch if you don't have a Bluetooth one with you). I'm not a big fan of its file access model however. There's not much concept of syncing — rather you download files from a source (SFTP, Dropbox or WebDAV), edit them locally, then re-upload. An option to edit directly into Dropbox or SFTP would be nice, but that's a bit of a personal preference.