Hi, I've some good news for u
. I'm working with that module for some months, and I have had no problem, except of course, that I can't make it work 1Km as the data sheet sais. I just make it work 100m. But that's another history.
Look, as bananasiong said , the module does not suport high(5V) for much time, it's just a matter of miliseconds and the output in the receiver fall(0V). So, u never gonna see the led turning on or off.
What I recomend is that you try with a microcontroler sending serial data. U will see the data going from the TX to the RX. The TX speed is up to 9600bps. I know it sounds a bit complicated, but is the only way u will see them working.
The other, of course is trying with an osciloscope and a generator.
There is some other modules, that supports slower transmitions, they are useless for my applications, but may be useful for yours,
See you