Although I agree that going with an infant in tow might not be ideal, if it's the only option, then make the best of it.
Strollers vary greatly in size and maneuverability. If this is not one of the larger ones, it could be a boon - you can tuck small purchases in the basket underneath. A baby is easier than a toddler or young child who is mobile! Be ready to nicely ask people not to touch him.
Take only what you expect to need for 2 or 3 hours for the baby and leave the rest in the car. You can go out and back in if you need to. Perhaps both you and the baby will be glad to be able to go out for a bit, sit and rest while he has a bottle, then go back in. This will also allow you to have a healthy, inexpensive snack and drink - which might be hard to do if the venue prohibits bringing anything in.
For yourself, comfortable shoes, light clothing with a sweater over, no coat. Depending on how you prefer to carry packages, either a tote or backpack for anything you pick up, whether it's vendor information or purchases. If you don't want to write on the prorgram, a small note pad, as well as a pen. We think we'll remember the name of a pattern/tool/fabric, but when you've seen so many, it's easy to forget.
I wouldn't carry a purse, but would use a waist pack or something simlar to keep your ID, money or debit/credit card secure as well as whatever basics you require (medication, tissues). Most phones will take pictures and are smaller than a separate camera, so if you have that option, be sure it is fully charged when you go in and leave the camera.
As long as he is tended to and not let to cry excessivly if over stimulated, tired, hungry or in need of a change, I'm betting that for every glare you get, you'll get just as many people saying the baby is darling. Remember that he might need to go out to the car for a break, and accept that. I'd rather go and enjoy part of the show, if having him there causes you to leave early, than not go at all!
Last - take a picture! Little ___ at His First Quilt Show!