You don't need another wireless router at your flat. All you need is a wireless adapter (D-Link). Most new Laptop computers come with built-in adapters, but if you are using a desktop you can buy one adapter for around QR 200.
Your Wireless router in flat 1 has to be a strong one to send signal all the way to the second flat. There are 4 or 5 different types of routers, so get the best one.