It might exist, but you cannot change it on a non-jailbreaked iPhone.
Assuming that your development webserver is on a Mac, why don't you simply use its Bonjour name (e.g. MyMac.local.) instead of myrealwebserverontheinternet.com?
No, an iPhone application can only change stuff within its own little sandbox. (And even there there are things that you can't change on the fly.)
Your best bet is probably to use the servers IP address rather than hostname. Slightly harder, but not that hard if you just need to resolve a single address, would be to put a DNS server on your Mac and configure your iPhone to use that.
This doesn't directly answer your question, but it does solve your problem...
What make of router do you have? Your router firmware may allow you to set DNS records for your local network. This is what I do with the Tomato firmware
Don't change the DNS on the phone. Instead, connect with wifi to the local network and you are all set.
At my office, we have internal servers with internal DNS that are not exposed to the Internet. I just connect with iPhone to the office wifi and can then access them fine.
YMMV, but instead of configuring the phone DNS, it feels to me that just setting up local internal DNS and wifi is a cleaner and easier solution.
In that case any dns lookups your iPhone does will use the hosts file of the machine Fiddler is running on. Note, though, that you must use a name that will be resolved via DNS. example.local, for instance, will not work. example.xyz or example.dev will.
As far as the server is concerned, it will behave the exact same way as if you had used http://myserver/mypage.php, except that the iPhone will not have to do a DNS lookup.