There has been too much Falco related advice. Falco players, you should know how to use your character, so fighting an average character like Doc shouldn't be a problem. If your losing to Doc, it's because of things he knows to look out for while fighting you. I (a Doc main) will hopefully give you an idea of what NOT to do.
Falco definitely has the advantage in this match up. Falco has got a better projectile, range and speed which can be used quite easily to destroy Doc. Doc on the otherhand, has Chainthrows, Gimp kills (Bair, cape), and many KO options.
Recovery really doesn't come into play during this match up because both of their recoveries suck. I believe Doc is better here than Falco because of his easy abuse of Falco's recovery (Cape and Bairs). Edgeguarding is a bread and butter type deal for Doc, so if Falco is off the stage, you better believe he's not making it back... although the same is true for Doc (blast you Falco's Dair!).
For the most part Falco will control the match. Using SHL sparingly and proper spacing, he can become a Doc's worst nightmare. Don't attempt to Pillar too often, because if you mess up, or Doc pivots his shield to mess up your L-cancel, say hello to a free grab, which is bad for Falco.
Attention all Falco players: DON'T GET GRABBED! Thats the biggest piece of advice I can give you, Doc will destroy you with Chainthrows -> Uair -> Dsmash (or Fsmash with proper spacing).
I would say, just keep moving and make as few mistakes as possible. The second you mess up, Doc will ownz you.
