You can't use a voltage divider that way.
The current to your load has to pass through one of the resistors. I your case, it has to pass through the 7k resistor.
Consider Ohm's law:
E is voltage in volts
I is current in amperes
R is resistance in ohms
Rearrange it to give current:
You have about 11 volts.
Divide that by 7000 ohms, and you have diddly/squat for current. About 1.5 milliamperes through the 7k resistor.
It won't help to lower the values of the resistors, either. You have current flowing through your voltage divider all the time. Right now less than 1mA.
If you lower the resistor values so that you get more current for the load, you will also increase the wasted energy. Your battery won't last very long.
What you need is a regulator.
A plain old linear regulator would be a start. They are easy to build using common parts. The common 7809 wouldn't work because your battery voltage is too close to the needed output voltage. There are many models of linear regulators available though.
Linear regulators also waste a lot of energy. This will shorten the run time of your battery.
A more efficient option would be to use a buck regulator. These are more difficult to build, but waste far less energy than linear regulators do.
As a simpler alternative, consider using 6 AA or AAA cells in series.
That gets you very nearly 9V, and is in fact the way 9V batteries are made. If you carefully saw open a 9V battery, you will find 6 smaller batteries inside. Each is a small 1.5V alkaline cell.
If you need to be able to recharge your battery, use NiMh cells. 6 in series will get you around 8V, which should work well enough for most things.