A lower valued external pullup can help speed up the risetime of an open-collector output stage, at the expense of drawing additional current during switching. In this case, other parts of the IR module limit your data rate, but they're present for good reasons, (noise immunity). In particular, the integrator limits the minimum burst length and the minimum time between bursts. Adding an external pullup (>= 4.7K) may help if you're trying to run a module near it's rated maximum speed.
You've probably noticed Vishay makes other IR modules rated for higher speed data rates, the TSOPx1xx series handles short bursts up to 4kbps, and the TSOP7000 data rates up to 20k. Notice the value of the pullup resistor in the internal output stage is reduced accordingly (TSOP12 -30K, TSOP11 - 25K, TSOP7000 - 10K). It's a tradeoff though, higher data rates mean less noise immunity and shorter transmission distances.