RF Transmitter Power

My RF transmitter RF Link Transmitter - 315MHz - WRL-08945 - SparkFun Electronics can be fed 12v to increase its range. It has four pins: - , +, data, and antenna. If I hook up an A23 12v battery to its + and - pins and hook the data up to my arduino will I hurt my arduino in any way. I'm assuming no, but want to make sure. Any guess on how long an Energizer A23 12v battery will power the transmitter?

Don't forget to connect the grounds.
Difficult to say about battery life, there is no current draw in the datasheet.[edit]Missed it - 11 - 59(!)mA, presumably continuous. [/edit]

The A23 is only rated at about 40-50mAh, though

The datasheet says 59mA current consumption at 12V, and the A23 data says 65 mAh (to 6V.) So about an hour, except that I don't think an A23 can provide 59mA at all; you're looking at essentially 8 tiny button cells in series, designed to provide tiny amounts of current. (The datasheet here (http://www1.duracell.com/oem/Pdf/new/21_OS.pdf) implies less than 1mA.)

Keyfobs probably use a capacitor and some clever power management to work at all...

What about it damaging the arduino? Would I be better off powering it with a 9v?