yea thats completely normal.. Cats always ( all the cats I have ever had anyway ) "play" with there prey before killing it. The last outside cat we had would hunt everyday even though there was always food for it in its food dish.. Its just in them to do so.. She would kill 8-10 rodents per week from the back yard and adjecent field. Mostly little shrews and a few mice ,etc. What was so odd was that she would kill them and not eat them, but instead bring them and lay there dead bodies at our back porch steps.. Kind of like a "Look what I did" type of thing.. I love cats. Cats rock.
Yes, they're so proud of their work! We used to have a cat that would jump off the porch to kill birds and then leave em in front of the door. My sister sure loved that when she was little, lol.