Bane seems to inject something into the Doctor's arms before kidnapping him. Is it like a sedative, so that he will be easier to kidnap or some sort of drug?
I don't remember anything being injected, but he did draw out some of the doctor's blood so his DNA would be found among the wreckage (injected into another passenger). Bane wants everyone to think that Dr. Pavel is dead, not just kidnapped. He's the only one who knows how to turn the clean power source developed by Wayne Enterprises into a bomb. His being kidnapped would raise a lot more suspicion than dying in an accidental plane crash.
The film's official novelisation confirms that Bane was drawing out the Doctor's blood with the intention of transfusing it into the dead body before the explosion and crash.
Since the body was burned, and with the teeth and bones damaged by the explosion, the searchers would be fooled that he was dead given that they would have to rely on a blood test to determine his identity.
Then he realized that the ominous black plastic bag was already occupied. Bane unzipped the bag to reveal the body of a stranger, who nonetheless looked vaguely familiar. It took Pavel a moment to realize that the dead man was roughly the same size and age as himself, with the same swarthy complexion and unruly white hair. There was even a distinct resemblance to their faces. I don’t understand, he thought. What does this mean?
Bane didn’t waste time explaining. He tore open Pavel’s sleeve, then reached into a hidden pocket in his own jacket’s lining, removing a length of surgical tubing. Hollow needles sprouted from both ends of the tubing. Bane kept a firm grip on Pavel’s arm. He palpated a thick vein at its crook. Wait, Pavel thought. Don’t…
But it was no use. Bane jabbed the needle into his arm, expertly threading the vein on the first try. Pavel winced in pain. He had never liked needles. What are you doing?
Swiftly taping the first needle in place, Bane inserted the other end of the tube into the arm of the corpse. Dark venous blood began to flow through it toward the dead man. Confused and horrified, Pavel watched aghast as Bane performed compressions upon the dead man’s chest, drawing the blood into the lifeless body.
The scientist felt sick to his stomach.
Less than a pint later, the obscene transfusion was over. Bane withdrew the needle from Pavel’s arm and gestured for him to apply pressure to the wound to keep it from bleeding out.
This pretty much matches what we see in the film's official screenplay, albeit with some extra commentary.
[A body bag is lowered into the cabin. Bane lies it on the seat backs next to Dr. Pavel and unzips it to reveal a body the same age and build as Dr. Pavel. Bane rips Dr. Pavel’s sleeve – pulls out a length of surgical tubing – pushes a needle into Dr. Pavel’s arm – runs the tube to the body’s arm … Dr. Pavel watches, horrified, as Bane starts compressions on the body’s chest, drawing Dr. Pavel’s blood across the tube and into the body …
An Armed Man pulls Hooded Man 1 up through the cabin and out. Bane stops Hooded Man 2.]