No he wasn't killed. What got shot in "The Impossible Astronaut" wasn't the Doctor at all. It was the Teselecta (the Justice Department ship seen in "Let's Kill Hitler"), wearing the appearance of the Doctor & putting on a "lightshow" to fake regeneration.
It was the Teselecta that was put into the boat & "burned". That funeral was a "cover" to allow the Teselecta to sink into the lake, change form (we presume) & then walk away unrecognised.
the Doctor was inside the Teselecta & (as he told Dorium in "The Wedding of River Song") he "never even got singed".