Why can Sailor Pluto be away from the Space-Time Door?
In the Crystal continuity it is unknown as it is a work in progress, and did not progress too much further from Pluto's introduction, so it is unknown for Crystal continuity if she will leave the door or not. There is still no canon material on the matter.

As to why she can leave the door, she has the power to seal off entire worlds out of the fourth dimension (the time dimension)(ref).

Since you need a time-space key to safely navigate fouth dimension, she could secure all keys, lock the access to the place where the keys were stored and leave for a short time. 

Probably her leave cannot be defined as permanent or temporary. Since the fourth dimension is outside normal time, she can safely exists in the fourth dimension and outside it:


  However, for all intents and purposes, in the manga the technicality of Sailor Pluto existing outside of time means she is able to be reincarnated as a normal woman while still existing back at her post at the Time Gate.(ref)


Sailor Pluto's racial status is also subject of controversy. While Endymion/Tuxedo Mask is from the Earth realm, Usagi/Sailor Moon is from the Silver Millenium race, the other sailor senshi seem to be reincarnated humans, Sailor Pluto is more of a goddess than a human:


  She is also stated to be the daughter of Chronos, god of time. (manga act 18, original anime ep. 82).


They made significant changes in Crystal from the original Sailor Moon works (like giving Tuxedo Mask an attack), so I wouldn't expect it to be identical, but to follow closely.

You can compare Crystal and the original making a parallel between the original Yamato series and Yamato 2099 that aired in 2014. They tend to follow the original work closely, but making adaptations and concessions to suit XXI century's scientific and social developments.