Double Switch but only Two Wires
If you have only one switched hot wire, you cannot control the light and fan separately just by getting a double switch. You would need two switched hots.

If this wiring is in conduit, you would need to pull one more wire from the switch box to the ceiling box. If this is NM, you would need to pull a new cable with another conductor a 12 or 14/3 + gnd (black, red, white, gnd).

One conductor (say the white, with a black mark or tape to indicate hot) would carry the always hot from the ceiling box to the two switches, one (say black) would take a switched hot to the fan and another (the red) would take the other switched hot to the light.    

Another solution to controlling the fan and light independently is to get a wireless controller which uses a single hot input (can use a switched hot and just leave the switch on) but has separate outputs for the fan and light. 

With only one switched hot you must use the pull chains. Leave the fan pull chain off and the light on and the wall switch controls the light. If you want the fan in addition to the light, use the fan pull chain. If you want the fan only, turn off the light with its pull chain.