How do I know what speed my mini is?
From the IDE, click on Tools>Boards, your are running at 16MHz if your selected board is "Arduino Pro or Pro Mini (5V, 16 MHz) w/ ATmega328"
The Pro Mini uses a ceramic resonator which is not as precise as the quartz crystal in the Uno and that may be a reason that SoftwareSerial can't cope with the baud rate. Can you use the hardware serial (on pins 0 and 1) for the GPS?