If I had $1500 to spend on a fixie, I'd pick up a classic steel-lugged ride from goodwill for $20. Add a $20 track cog, and use the remaining $1460 to take the girl to Europe. Or the little girl to Disney. Or pay the mortage. Or any one of dozens of other things.
Better yet, just buy a fixed wheel for your current ride and do the switcheroo.