Software serial is if anything going to be slower, because the hardware USART does a lot of things (like automatically generating start and stop bits) that the software serial library has to emulate in software.
For the timeframe of <1mS, you should be able to do everything with the default arduino functions with plenty of time left over.
Note also that you can set the serial baud rate faster than even the 115200baud listed as the max baud rate in the Arduino IDE. I've set the baud rate to 250000 and still been able to send and receive with no errors, although I had to optimize the code pretty carefully in some places. Not sure how well Processing will support those speeds, though.