Hi Rebecca,
If i'm honest, I don't think that you will be able to get to Planet Hollywood in time for a 10.15pm dining reservation.
IllumiNations: Reflections of Earth lasts for approximately 15 minutes and once the show has finished, you will need to exit the World Showcase and walk back towards the entrance of the theme park through Future World to reach the parking lot or bus stops. Bearing in mind that a large amount of other guests will also be trying to exit the park at the same time as you.
You would then need to drive or wait for Disney transportation in order to get to
Planet Hollywood which is situated at Downtown Disney West Side.
If I were you, I would keep checking the Walt Disney World online dining system
HERE for openings at Planet Hollywood on a different day of your trip or perhaps you could consider watching IllumiNations on a different night?
Wishing you a magical holiday!