Does my ceiling fan's down rod need extra support?
Look in the parts for your fan and see what is the longest pipe that comes with the fan. You will probably find two pipes, but even the longer would be much shorter than 24".

Go online or to a "fan store" and get a 24" pipe specifically made for your fan. It will be installed in place of the shorter pipe that comes with the fan and will come painted to match your fan.

How tall is your ceiling? Be prepared to give that measurement to at the fan store and they might advise you to get a different length pipe--either shorter or longer than 24". As a rough guide I would say that a 24" support rod would be about right for a 10' ceiling, depending on how far down your light kit projects and what you preference is.   

The wires that come on the fan are much longer than needed for short pipes and are probably long enough for a 24" pipe without having to add extra wire, but you will have to see what the instructions say.

EDIT

The modern cheaper fans (e.g., Hunter) can be installed at the location of a box which formerly held only a light fixture if there is a ceiling joist next to the ceiling box. The fan installation kit has a bracket with long screws which go into the ceiling joist which a box is nailed to.

But if the joist is not adjacent to the ceiling box, then the box may well be a light duty one which is on a light metal bar which would not support any fan. In that case the existing box and bar would have to be removed through the existing hole and a fan box with bar installed (through the existing hole).

EDIT2

For example see Down rods for Hunter fans

EDIT3

Note that if you need to substitute a fan support bar for the existing one, you need one which is designed for retrofit through the existing hole. There are some fan support bars which will only work if there is no drywall in place. These are much cheaper but they cannot be inserted through an existing 3.5" or 4" hole in ceiling drywall whereas the retrofit ones can be.

EDIT4

In case of failure of the primary fan suspension safety cables will provide a backup. Safety cables may be required in seismic zones, and in certain applications such as schools, daycare facilities, nursing homes, etc.
Panasonic info on safety in fan installations

None of the fans I have ever installed, or had installed for me, has a safety cable.