Streaming video output through WLAN?

Recently, my desktop monitor broke. Since I have to wait some time for it to be repaired, I have coected an old TV with a pretty poor resolution (1366×768) and with a screen to big for me to comfortably work or play on without headaches. However, I have a laptop with a better screen (1080p and ideal size). I know it's possible to share the screen using various programs. The problem is that I don't want to mirror the screen, as it would have lower resolution (that of the old TV). Can I simply send the 1080p video output through WLAN to my HD-screen laptop, bypassing the low resolution monitor? If yes, how can I do that/what program can do that?

Thanks in advance.