I used to fly with son all the time when he was a baby and all I can say is: GET THE EXTRA SEAT! Seriously, even if you end up holding him on your lap for most of the flight, just having the extra room to sit him down for a minute while you get out a snack, etc. is absolutely worth it.
The flight from Chicago to my parents in Ohio is about 45 minutes. I know an hour and a half or 45 minutes doesn't SOUND long, but if you are holding the baby, even in a sling, the whole way, you are going to get off that plane with aching arms and back.
Also, if - god forbid- he gets sick or fussy, you really don't want him right in your face that entire time, without being able to put him down for just a few minutes to get a drink of water or eat an apple.
Last but not least, think of your fellow passengers. Everyone knows that babies can cry on planes, it is part of life. But if you are squished right into a seat beside a crying baby... that can just make the whole flight unpleasant- especially if mom is jockeying around trying to get the spare binky out of the diaper bag under the seat while Baby is drooling on your armrest. ;)
Take your stroller to the gate and make them give it to you when you deplane. Do early boarding and get the extra seat! Have a great trip- I did this often with my son and if you're prepared, it will all go just fine!