If you compare the nutritional label for whole milk vs. 1% milk (since that's what we have at home), there is a big difference in calories and fat.
It's really critical for kids under 2 to have that fat for proper brain development.
Obesity is a really hard topic to wrap our brains around because we only understand a portion of it scientifically. There are certainly genetic factors (we all know people who can eat ANYTHING and never change dress sizes), there are metabolic factors, calorie consumption (eating) vs. calorie expenditure (exercise), hormones, behavior, etc.
My previous company is preparing to submit several new drugs to the FDA for approval all based upon hormones produced by the gut, the brain, and the pancreas that have an impact on body weight.
I believe part of why our daughter is in the 97% in weight is because she would literally drink as much Whole Milk/day as we would let her. We moved her to 1% a month before her 2nd birthday after talking to the pediatrician and getting his blessing.
As for childhood obesity, the main culprits are diet (or lack of a good diet) and lack of activity. When we were kids, if we said we were bored, our parents would tell us to go outside and find something to play with. The world is a little scarier place these days, and a lot of parents aren't as engaged with their kids.
Your daughter, at 18 months and being on the small size shouldn't have any problems with whole milk. If she begins to fill-out more, though, I'd have a discussion with the pediatrician.
If you've missed it, watch Jamie Oliver's Food Revolution - it talks about a lot of this: http://abc.go.com/shows/jamie-olivers-food-revolution