You have run into a common problem now-a-day. The problem is most of these modern communications chips no longer allow the user to access the IF frequency before demodulation. The newer ICs either use soleley digital filtering of the IF, or use a zero IF scheme. So...you are sending 1.2 kbaud, and should have at most a 5 khz IF bandpass filter, but are forced to use 58 KHz.
So what can you do?
Yes, you can put a LNA in front of the chip. Noise floor is -174 dBm/Hz +1.1 dB NF + 10 log 58,000 = -125.3 dBm. So you are not going to do any better than that, and probably not even get that due to other noise sources in the chip. But you will probably get better than -111 dBm. I would personally do the LNA and then a bandpass filter centered at 315 MHz between the LNA output and the chip....to limit out of band noise causing trouble. Also, you might have trouble if the transmitter gets too close, due to all that system gain.
You could change ICs. Melexis has some IC's that allow access to the IF frequency at 10.7 MHz. Throw a narrowband ceramic or crystal filter in there and it will help a lot (although you will need accurate transmit and receive LO frequencies!). Microchip has a reciever like that also.
Anybody know of other "modern" Reciever ICs that allow access to a 10.7 MHz IF for filtering?