First things first. Did you check the little box at the beginning of the installation of Peach OSI to allow for Peach to connect to your WiFi during the installation process? This is the most common reason for WiFi not being setup during the installation process. If you tick on that box you will be presented with a box to fill in your WiFi password prior to installing Peach. Really, it is best to have any and all gadgets (mice, keyboards, external drives, etc.) connected before you begin the installation of any OS, not just Peach. That's because many devices can be automatically setup during the installation process or else they may have to be setup manually after the installation. In setting up these devices during installation the OS looks at what hardware is connected to the PC and then it attempts to go out on the web and find the appropriate files and drivers for the OS to communicate with that or those particular pieces of hardware. If there is no connection to the internet available at the time of installation then the installation process of the OS is crippled to being able to setup most devices (especially no-standard devices) during the installation process.
One more thing of importance. If you gave the "live" process your WiFi password prior to the installation attempt - try the installation again without giving the"live" process your password. The reason being that if you gave the live process your WiFi password then you won't be given the box to check for WiFi during the install process. Be sure to also check the box to allow Peach to download any current updates while installing.