Ok - generally this function will use sendmail (on *nix systems anyhow).
Now this will automagically set the reply-to header for you, which will be the system's setup reply-to, in your case - "nobody@mydomain.com". If you try to set this as a header from PHP, you will tend to find that it will remove it from your mail, since this has security implications where people can spoof themselves as different email addresses, so sendmail makes this trickier to do.
Now - the 5th param in mail() is to setup additional parameters which can be sent to sendmail and one of these (if you look at the *nix man pages for sendmail) lets you set the reply-to header. Unfortunately, not all users can do this, and the mail address you try to spoof yourself as must be a trusted email address by the system. This means adding the mail address to a particular config file somewhere on your machine (usually only root users can do this). I cant remember where exactly you add this, but the sendmail docs should tell you.
Of course - this is just one way of "skinning the cat", and as we all know, there is generally more than just one way.
The second way is a bit lengthier and quite a lot more involved, but gives you loads more control over your mail and how it's sent, where you send it through etc (this way assumes your firewall will allow your PHP scripts to make an external connection to an SMTP server- port 25)
This solution is to use a script (either from somewhere else, or create your own) that connects to an SMTP server and allows you to send your mails like that. These scripts will have to be able to communicate using the SMTP protocol, and determine the state of any commands sent.
Once you have this, it is generally easy to send your emails. You have no restrictions on any headers you can set etc, so, theoretically, your emails can come from any address etc.
As I say - there are probably several scripts out there which will handle the hard part of the comms for you, and allow you to simply specify an SMTP server and then you just call a "mail" function to send your mail as usual. I myself have written classes which do this, so it cant be that tricky 🙂
Good luck