Q:

How should I handle a door the players know is trapped, but the characters don't? 

My group and I have recently stumbled upon what we, being inexperienced with FATE, perceive as somewhat of a conflict within the game's approach and rules itself, which I hope someone could shed some light on. 
Assume the following scenario:
The group reaches a door in a dungeon which is trapped, and they have to make the choice of opening it or seeking another route.  
FATE suggests telling players outright via an aspect that the door is trapped.  At the same time, however, it also includes the action "create advantage", which would normally serve to let characters 'discover' an aspect. 
Now this presents a bit of a paradox.  If the aspect is already on the table, there is no reason for the player to take a "create advantage" action.  If it is not on the table, then the GM is consciously hiding a key information from the players, which is heavily discouraged by the rulebook and the designers.  
How does one deal with this?  My initial idea would be to put aspects on the table that are clearly marked as 'hidden' to the characters, but that the players are aware of - basically pieces of information that give the players an indication as to where to look, but require separation of player and character knowledge.  Failing a create advantage action might convert "(hidden) Trapped Door" into "(visible) Missed poison dart trap in the door" or somesuch.  
Is this the right way to go about it or is there another way that we might have missed? 

A:

So, let's set things out here. 

The door is trapped. 
The players know this. 
The characters don't. 

How does one deal with this? 

The oblivious characters carry on as normal.  If they have no reason to suspect the door is trapped, they probably walk straight into it. ( The trap that is, not the door.) 
If they do suspect it, and it's reasonable the characters would actually suddenly investigate this particular doorway, then they'll probably do that investigation.  If they find the trap, they might want to disarm it, or find another door.  This is all narrative considerations at this point.  When you want to dip into how this is handled mechanically, Fate's toolbox offers a bunch of options. 
Given you've made the trap an aspect, it might be appropriate to model the investigation as a challenge to overcome that aspect (the players may use Notice, or Investigate, or whatever is appropriate).  Then, if they want to disarm it, that could be another challenge.  If they want to find another door instead, and it's justifiable, they could create an advantage and put an aspect like Another Door!  How Useful!  on the scene - then walk through that other door they didn't see before. 

Is this the right way to go about it or is there another way that we might have missed? 

It's a perfectly OK way.  However, there's another option: use the Bronze Rule and model the door as another character.  Make it be very Sneaky (in Accelerated) or have good Stealth (in Core).  Its High Concept might be Sneakily Trapped Door, and when the players walk through it, it'll attempt to attack them or create advantages on them (Poisoned!  or Winded!,  etc). 
It should have placed a Well Hidden Traps on itself using its Sneaky/Stealth skill: this way they'll notice the door, but not its traps, and to notice them, they'll have to appropriately overcome that aspect.  It ought to have a short stress track, and they could make attacks via Craft or other appropriate skills to disarm the trap - or just, y'know, totally smash it to pieces. 

A:

I'm not sure which ruleset you're referring to, but I think you've misread. 
From Fate Core, from the section entitled Secret or Hidden Aspects:

Some skills also let you use the create an advantage action to reveal aspects that are hidden, either on NPCs or environments—in this case, the GM simply tells you what the aspect is if you get a tie or better on the roll.  You can use this to “fish” for aspects if you’re not precisely sure what to look for—doing well on the roll is sufficient justification for being able to find something advantage-worthy. 

The next paragraph does contain some text related to your premise but I believe you're missing some things.  Emphasis mine. 

Generally speaking, it is assumed that most of the aspects in play are public knowledge for the players.  The PCs’ character sheets are sitting on the table, and probably the main and supporting NPCs are as well.  That doesn't always mean the characters know about those aspects, but that’s one of the reasons why the create an advantage action exists—to help you justify how a character learns about other characters. 

Essentially, the only aspects that should ever occupy (misappropriated) Schrodinger space are those that belong to characters.  And since players essentially have no say in the behavior of NPCs outside of compels, simply refusing to allow the players to make use of aspects that have not been revealed through play solves this problem. 

A:

Although I agree with the others in that you can definitely have hidden aspect.  However, you could handle this with an event based compel as well.  Something along the lines of: 

Because the door is booby trapped and you do not know about it, it makes sense that, unfortunately, you would trigger the trap while opening the door and be hit by a poisoned arrow. 

But more interesting of course.