Remote Desktop will do it, but Mac OS X Leopard and higher include screen sharing as a basic feature of the OS for free. Only requirement is that you both run at least 10.5. Search the help file for Screen Sharing for details, but basically you enable the sharing on your brother's Mac in System Preferences and then connect using the network browser or Connect to Server in the Finder.
You can also share your DVD in the other direction, from your Mac to your brother's, to be able to install from it.