Does this camera have a timer to set to take a picture automatically?

yes, it has a timer:

Using the Self-timer

Changing the Self-Timer Settings

With this function, images are shot 10 or 2 seconds after the shutter button is pressed. This is useful when you want to take a memorable photo with everyone including yourself in the picture. The self-timer can be used in any shooting mode. In addition, you can set the delay time and number of shots (Custom Timer).

1. Press the <FUNC./S button and use the ^ or v button to choose (Single Frame).

2. Then use the or buttons to choose , < or > .

* When the shutter button is pressed fully, the self-timer will activate and the selftimer lamp will blink.
* When the self-timer is set to 10 sec or 2 sec, the shutter activates in 10 or 2 seconds after the shutter button is pressed fully.
* With the (Custom Timer) option, the specified number of shots are taken after the specified delay when the shutter button is pressed fully. You can change the delay time (0?10, 15, 20, 30sec.) and number of shots (1?10). When [Delay] is set to 2 or more sec., the self-timer sound begins to beep 2 sec. before the shutter releases. When [Shots] is set to more than 1, the self-timer sound only beeps before the first shot.

To Cancel the Self-Timer

Follow the same steps as above and return the setting to (Single Frame).