Trying to install Ant but getting -bash: brew: command not found
If brew doctor doesn't run, then you have some breakage in the PATH variable on the system or you need to re-run the installer package, perhaps cleaning up things according to the support site for homebrew.

You can check where the brew command is with:

which brew
type brew


Both of those should point to a command located at: /usr/local/bin/brew and the path /usr/local/bin should be in your path variable. To test that, quit terminal and open a new window. The set command below should look like the one I pasted with "mac" and "me" different for you in all likelihood.

mac:~ me$ set | grep -i PATH
PATH=/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin


Since this is how the system should be set up out of the box, if you have made modifications you'll want to look over the site for ways to debug a broken path. Your text seems to indicate that the path is set correctly, but that's the cause of command not found or the brew script itself is somehow corrupted - but that script is in /bin/sh not bash so I would expect a different error if it's messed up in some manner.