Dude, it would be a lot more weird if you walked her into the Women's bathroom! And probably illegal! LOL. I take my daughter into the Men's room to change her diaper from time to time. My wife usually does it, but since we now have 2 kids, I find I'm doing more often. It's no biggie.
I do know where you're coming from though. I was changing my girl in the Ripley's Aquarium in Myrtle Beach ... a boy (probably 10 years old) commented "Daddy look that man's changin' that baby" ... but in a way that suggested that it was a completely foreign thing to him. I laughed in pity.