if you leave out your transmitter and receiver and connect two arduino boards directly (by cable), it is important that you not only connect RX to TX but also ground to ground. did you do that? the board-to-board thing should work reliable before you start on the over-air transmission.
about the HI/LOW voltage:
i don't know if there is a page on arduino's electronic specs. but i think that the atmega8 and arduino use TTL standard. see wikipedia for an explanation. logical values (0 or 1) are defined as ~0V and ~5V.
i think the max856 might be the IC specially made for your needs. but as i said, a transistor plus a resistor should be enough to amplify your 0.8V signal to a 5V. maybe you should start another thread in the forum to find somebody who can help you with the values/models. though i never needed to boost a signal yet, it seems quite a standard problem to me. (with an easy solution)
your pdf at conrad.at isn't reachable at the moment. so i searched on google for similar modules. one thing you could try (at your own risk!) is putting a 10kOHM between +5V on arduino and the RX pin, where your receiver is connected to on the same board. if your receiver's output is "open-collector" it might work. in this case the resistor will work as a pull-up resistor and boost the HIGH signal.
but you should definetely switch to a lower baudrate, say 2400bps. AM modulation is slower than i thought at first. similar products to yours recommend 2400 to 4800bps maximum.
//kuk