So I've been curious about this, so I did a little research. Here's my results in case anyone was curious as well.
I'm using an iPhone 4S and Instagram v2, so if you're not, your sizing will be different. I tested this using the default Camera app, Camera+ and Instagram, with all the settings set to save the max resolution possible.
Here were my results (all in pixels):
Apple Camera App only: 3264x2448 (max iPhone 4S size - 8MP)
Camera App photo imported into Instagram: 1264x1264
Camera+ only: 3264x2448 (max iPhone 4S size)
Camera+ photo imported into Instagram: 1361x1361
(Oh and if you accidentally end up in burst mode, your photos end up super tiny - 480x480px once imported into Instagram. I don't recommend doing that.

)
Photo taken with Instagram: 2048x2048 (max Instagram size for the 4S, it's lower for the iPhone 4 & 3Gs)
Soooo...apparently the output size in Instagram does depend on what app you use to take the photo. The good news is that all of the photo sizes are over 4x4 inches at 300 ppi so they should still be easily scrap able. You can also set up Instagram to save a full resolution copy in addition to the edited version when you take a photo using Instagram rather than importing a photo into it if you want a bigger size.