If you used a resistor/capacitor circuit that is started to be charged when the IR pulse is sent out, the voltage on the circuit should be proportional to the round trip time of the IR pulse when it returns.

Circuit Idea 1
Sub Systems:
Use an IR LED as the transmitter.  A photodiode with ambient light cancelation as the receiver.  A capacitor as the timing element.  A fast sample and hold circuit.  An analog to digital converter for measuring the capacitor's voltage.

Opperation:
Shunt the positive side of the timing capacitor to ground.  Wait for it to settle.  Pulse the led really fast and at the same time release the shunt to ground on the capacitor.  The capacitor is charged by a resistor to Vcc so it charges at a fixed rate.  When the return IR pulse is detected by the photodiode circuit, it triggers the sample and hold circuit to take a sample.  The ADC then digitizes that sample to give the distance.  Actual distance can be calculated after calibration.  Repeat the cycle for a few times to get an average, but throw out samples wildly out of range of the others get a better distance.  With proper circuit design this should be repeatable as fast as the ADC can be run with the time limit of discharging the timing capacitor as the other limit.

Circuit Idea 2
PWM design, The round trip time of the IR signal (or timeout limit) is the time a charge transistor is allowed to provide current to charge a capacitor that is being discharged to ground via a resistor.  The voltage this circuit settles at is proportional to the avearage of the last few samples.  Sample the circuit through a sample and hold ADC to measure the distance.

Circuit Idea 3 (Similar to #2)
Fixed frequency switching powersupply circuit.  Then source transistor is turned on when the IR pulse is sent out.  It turns off when the pulse returns or it times out.  This will give an output voltage that is proportional to the distance to the detected object.