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Your relay isn't controlling anything. I think what you want to do here is put one side of the relay to +12V and the other side to the +V of the pump. I also think the common of the ULN2003A should be connected to your GND (coil is controlled with 12V and GND).
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I was planning on switching the pump on and off using a switch in my vi. When the switch is on the output voltage from the daq is 5V and when it is off the output voltage is 0V. Is this a poor approach? Do I require the relay at all if all i need is a 12V output voltage and 300mA output to drive the motor of the pump? Thanks
Please place a small help wanted ad at your engineering school and request the help of electronics student. You need to understand that you are not switching anything at all no matter what the logic out of the daq device. Yes, a very poor approach.