Hall sensor for slowly varying magnetic fields
Would chopper-stabilization of the amplifier in the Hall sensor
  mitigate the 1/f noise?


No, because the sensor internally has a chopper amplifier: -


  Chopper stabilization is a unique approach  used to minimize Hall
  offset on the chip. Allegro employs a  technique to remove key sources
  of the output drift induced by  thermal and mechanical stresses





  Does this noise generally come from the Hall element itself or from
  the electronics (presumably amplifiers) present within the Hall
  sensor?


Now that's a good question and I don't think anyone can tell from reading the data sheet but I'm sure if you low-pass filtered the signal you would remove a lot of noise.

For instance, the spec says the noise is 1.3 mG / \$\sqrt{Hz}\$ and this means that the noise produced over a 1000 Hz bandwidth is 1.3 mG x 31.62 = about 41 milli gauss and given that 1 gauss is one ten-thousandth of a tesla, the noise is equivalent to a magnetic noise of 4.1 uT i.e. not very much compared to your measurement range of 50 mT.

Of course, if you are looking at this noise on an o-scope with 50 MHz bandwidth, it will look like equivalent to about 1 mT but you don't need the bandwidth so just slug the output with a simple RC filter of a few hundred Hz cut-off.