I think it depends on the crowd attending. My family and my husband are beer drinkers... our friends drink beer, and my husbands family are wine drinkers. For my son's first birthday, we had it at a park district, and it was only a few hours long, so alcohol was not in the equation. Is your party an 'open house' with no specific end time?
Personally... I think as a host to any party, you take into consideration what people want to drink by offering a variety... pop, diet pop, water, juice boxes for kids, etc. And in my opinion, offering beer or wine is just one of those things that a good hostess would offer knowing that her guests drink it. I don't think this needs to be about morals... it's really up to the parents to teach their kids about alcohol drinking, doing it responsibly, etc.
You could get just a couple cases of cans... which are less expensive than bottles, say Bud Light and Miller Light, and that should keep the drinking to a minimum...
I threw my husband a surprise 30th birthday party (no kids though) and spent 700 bucks on alcohol for 60 people... by 3 am, and quite a few cab calls later, there was only a few bottles left... I wouldn't encourage that kind of party for your son's first birthday :)
I would offer the alcohol, in a limited amount.