Moiraine had done extensive research throughout her life leading up to her entering the Waste, and it is plausible (though admittedly unprovable) that she had studied the origins of the lore surrounding Snakes and Foxes. Her letter, if nothing else, proves she had made that connection before her trip through the second doorway.

She was familiar with the fact that a second doorway existed from her trip through the Rhuidean rings and throughout her travel out of the Waste. She would have noticed the difference between this doorway and the one in Tear.

She also must have noticed Mat's changes after going through the doorway. His sudden intimate knowledge of the Old Tongue and battles are telling that something momentous happened to Mat in Rhuidean, but having the foxhead medallion could have been the clue that told Moiraine exactly what happened to him. This knowledge could have very well tipped her off that the creatures on the other side of this doorway work differently than the ones from the Tear doorway.

It seems more than plausible that she was armed with enough knowledge of the Eel'Finn that she may have faired better in her dealings with them than you give her credit for.