It's your family and your trip, so it's ultimately up to you and your wife, of course. However, if your asking what our OPINION is, here is mine: leave her at home.
Myself, If it came down to either taking the kid or staying home, I would choose to take the kid. However, if it was a choice between going with or without the kid, I would choose to go without him and leave him with grandma and grandpa.
As others have said, having a 15 month old (or any child anywhere close to that age) changes things drastically. Many people here are fine with that and are happy to adjust their plans to accomodate an infant. I'm not. I'm not fine with having to get back to the hotel early just to put a child to bed when I would rather spend the evening at the park. I'm not fine with having to skip rides, or do the parent/child switch thing all the time because the child is too small to ride. I'm not fine with having to take a million differnent breaks for naps, feedings, diaper changes, etc. And I'm not fine with the prospect of my child being one of those dreadful brats that makes a huge scene on the bus or in line. So, for myself and my wife, we feel like having a child along is just bad for the child (because he can't do much anyway) and the parents who can't do as much with a child along. So we prefer to leave our son at home until he's 4 or 5, and then take him.
Like I said, it's your choice and I don't fault any parents who choose differently from us. But it's simply my opinion that bringing a child of that age along will not make the trip better for anyone.
<edit> I guess I should rephrase that last part because many parents here can testify that they think their trip IS better by bringing their little ones along. And that's fine. As long as they have a good time doing it the way they do it, more power to them. What I should say, I guess, is that in my opinion for MY vacation, the presence of an infant/toddler along will put a damper on the trip, for the reasons I gave.
Parenting is a joy, don't get me wrong. And I realize that changing diapers and having to get back early to put the baby to bed, etc, are all parts of parenting, and I don't regret becoming a parent.
But as for me, when I go on vacation, I want to leave ALL responsibilities behind for that week, as long as we are fortunate enough to have someone back home who can watch our child.
I want a week where I don't have to worry about getting up to go to work in the morning; or having to go into work that night, or where I don't have to mess with putting the dog out. And yes, I don't think there's anything wrong or shameful with wanting a vacation from the responsibilities of parenting. A week where the wife and I can go out and do what we want, when we want without wondering how the baby will do, or what time we need to be back to put him to bed. A week where we don't have to mess with changing diapers or lugging around a diaper bag. Basically, a week where the only thing we have to concentrate on is being at our ADR's on time, or getting to the park before it gets too busy, or getting to Splash Mountain in time for our fastpass.
Surely some will strongly disagree with me on this, and that's fine. But I think there is nothing wrong with leaving EVERYTHING behind...including the responsibilities of parenthood.