Micromice use reflected light to measure distance. Is that your application?
The same technique works for object detection, after all robot mice must not bump into things :-)
According to the spec of the devices you reference, the emitter spec is:
Continous forward current: 50mA
Power Dissipation 75mW
Peak Forward Current (300pps, 10us pulse): 1A
So, pulse the emitter at near 1A to enable sensing from further away. If you have a microcontroller, that is easy to arrange. Others are better qualified to offer the pure electronic solution.
One microcontroller approach uses a capacitor, sized to deliver 1A for a couple of times more than 10us, and a bipolar or FET transistor to switch power through the emitter.
Searching for "micromouse pulsed emitters" will turn up several places with all the details you might need.
Light intensity is proportional to 1/Distance^2
So the intensity will need to be 4x bigger to double the distance.
Assuming the device is linear, the difference between 50mA and 1A is a factor of 20. Sqrt(20) is about 4.5x, which is quite a big improvement, well into your hoped-for distance.
Edit:
The emitter signal is modulated so that stray light can be detected and ignored. The Sun, is a very large source of IR, and can easily confuse or 'blind' the detector.
A simple technique to use the modulation is: measure the detector value with the emitter off, measure the detector value with the emitter on, then subtract the first from the second. If the answer is close to zero, then either the light beam is blocked or it is being blinded and can't detect a crossing object. For a "burglar alarm", that might be enough to trigger it.
A much better approach:
Having said all of that, IMHO a much better approach, which could be implemented without an MCU but it might be complex, and which would give more than 12 feet (4 metres) is to use an IR remote control sensor as the receiver.
They are mass produced by companies, for about $1-$2 e.g. Farnell's IR Receivers, Digikey's IR Receivers RS IR Receivers Sparkfun IR receivers
I have controlled TVs from more than 30 feet away with a single emitter, using a TV-be-gone. So the receiver works extremely well.
However, this is off-topic.
It appears that each emitter is an IRLED and that they're all emitting all the time.
The detectors, on the other hand, work individually and each one only turns ON when it's hit with IR. Since their V1's are connected to +5V, when they're OFF no current will pass through them and the voltage across their 10k ohm pulldown resistors will be close to zero volts (GND).
On the other hand, when they're turned ON by IR, current will pass through them and the pulldown, with the result that a voltage will be developed across the pulldown which will be sent to the Arduino, letting the Arduino know that a sensor has picked up an IR signal.
The sensors appear to be used to detect IR reflected back from the emitter.
Best Answer
That circuit is not very good for driving the LED. In fact it is very likely to damage it and too slow to drive the LED with the required carrier frequency. As anyone can try to copy your design, you should fix the circuit as most likely people don't understand why the circuit works poorly or burns up LEDs.
The poor range can be due to LED being already damaged as it is driven without a current limiting resistor in series. Replace the LED and this time use a resistor in series to prevent damage to the LED.
If that does not help, another issue can be that the transistor might not be able to turn on and off quickly enough at the necessary carrier frequency. The transistor can be extremely slow to turn on and off with only 10k at the base. Also the 10k can be too high a value even at DC to drive the base hard enough to get enough LED current - it is possible that you would get better range without transitor and only the LED with 100 ohms in series. In an actual circuit, you would use smaller base resistor to get fast enough LED drive and then use a series resistor with LED to keep current high but not too high - IR LEDs are typically pulsed at 100mA or so.
Also check that you are using the correct IR carrier frequency for your device. There can be a significant reduction in the range if the carrier frequency is wrong.