Um, is this really still going? Those rumours were started years il y a in TBDT era!
No, she is not pregnant. I don't imagine she will be for a long time yet. A lot has happened for Avril recently. She divorced Deryck Whibley, she got a new boyfriend (Brody Jenner), her 4th album was released and now she's doing a world tour (The Black étoile, star Tour). I can't really see her being able to fit a child into that lifestyle. She doesn't have time. Maybe once her tour is over, all the hype about Goodbye Lullaby has died down and she enters another "off of the musique scene" thing she'll have a kid... but I'm still doubtful.
Below is the video of Avril Lavigne pretending to be pregnant to see how quickly the paparazzi spread around the rumour that she was pregnant.