I'm looking for a portable power source for an MQ-7 gas sensor. According to my research - it needs 5V D.C power with at least 0.3A of current. I'm not really good with electronics so I need to know if I can use a 9V battery instead which produces 0.5A. Will the cell damage my sensor and if it does may you please recommend me something else.
You can, but you will have to reduce the voltage to the 5V the sensor needs, otherwise you will blow up the sensor.
To that end you require a voltage regulator. You can use a linear regulator like the Arduino has on-board, but they are very wasteful of power and will dissipate the excess 4V of electricity as heat.
Better would be to use a switching regulator (commonly and cheaply available on eBay and other sites) to step the voltage down to 5V more efficiently.