QRE1113GR Reflective sensor biasing
The diode forward voltage is about 1.2 volts therefore, from a 3V supply, the current will be (3 - 1.2)/10k = 0.18mA. Given that the device data sheet tends to use 20mA for a lot of the specifications I have to say that 0.18mA appears very low.

At this current there is nothing in the data sheet that really tells you how it is going to perform. For instance figure 2 tells you what the anticipated collector current is for a given diode current - it's almost impossible to predict with a diode current of 0.18mA.

Then figure 1 tells you the collector current versus distance of a reflective mirror for 10mA diode current. Again you are off the scale with 0.18mA and impossible to predict.

If 4 to 10 mA is too much then consider pulsing the diode to give a big peak of current with an average value that is low. Of course this complicates things but, at 0.18mA I'm not sure you'll get this to work at any distance from an object reliably.