The 1911 pistol and the 1911A1 pistol were designed to be carried with a round chambered, the hammer back to full cok and the slide safety engaged. The pistol, at that point, was and still is considered fully safe as two (count'em boys, two) safeties are required to be disengaged before the pistol can be fired. That makes the almost 100 year old design of the 1911 to be safer today than many of the other pistols available.
It is not recommended to carry the 1911 or 1911A1 on half cock. The half cock notch on the hammer of those pistols is shallow and not designed to safeguard the pistol from accidental discharge if dropped. It simply hampers the full fall of the hammer to prevent accidental discharge if the hammer slips from full cock when a round is chambered using the slide release. This is seen in some pistols where less than judicious trigger work has been performed.
It has been shown in time trials that leaving the hammer on half cock costs the shooter another .5 - 1 second time in bringing the pistol to bear and firing two shots to the target in close quarters drill. That could cost you your life.
The 1911 was designed to be carried with a round chamberred and fully cocked and locked. It is then in its safest, most reliable and rapid to present condition. Mikey.