I'm not familiar enough with XP to give you tips on how to run it with XP's native DOS emulation (i.e. what Compatibility Mode settings to tweak), but if nothing else you can always try running it in
DOSBox, an open source DOS emulator you can download for free that runs most Sierra games from this era flawlessly. I've also noticed that sometimes old installation programs are more finicky than the games themselves, so it might even be the case that after installing Island of Dr. Brain using DOSBox, you would be able to play the game normally with XP's DOS emulation, if for whatever reason you'd rather do that. However, DOSBox might run the game at a better speed anyway, since it allows for adjustment of CPU cycles.
Of course, with a little more information about the error you're encountering, Ghost Rider or others on the board might be able to offer you tips that will allow you to forego DOSBox entirely and install ordinarily in XP, if that's your preferred solution.
Take care,
-Luke