Not good idea:
1. Those units are meant to be installed permanently. The heat exchanger you show on your picture is bolted to a bedroom wall and connected with a pump [installed outside of wall] by wires and pressure hose. Then the system is filled with refrigerant [gas]. Could be relocated, but then you have to have a technician installing it and charging with gas.
2. It will cost you in the area of $ 1,000, possibly more.
3. If you buy inexpensive unit, it is not energy efficient, high electricity bills. If you buy Panasonic Inverter, it is great, but not cheap.
Since you still have to pay rent, it may be much more economical to rent a place with AC unit.
