Welcome!! You have a beautiful machine!
In spite of the "White Peerless", it appears from the needle chart on ISMACS that this machine is made by AG Mason. It takes a 20x1 needle, which is obsolete, but can be found on the Internet. There are those that believe AG Mason is nothing more than a badged White, but AG Mason was a company of it's own accord until 1916, when it was absorbed by White. (I'm going on memory, so that may not be 100% accurate as to the date)
Do you have any bobbins for the machine at all?