I get 0.111 mAh. There's 1000 ms in a second and 3600 seconds in an hour.
The rated capacity of a 9V battery might be something like 170mAh. That should get you 765 watering events (turn on + turn off) but that rating is only valid for very low currents. The best way to use the battery is to draw a low, constant current. At high current there's a lot of power lost in the internal resistance of the battery.
Open up a 9V battery and you'll see lots of very very skinny cells inside. They can't pass a lot of current without heating up. (Losing power.)
So at that kind of usage, you will get much less than half of the claimed capacity from the battery.