This is actually two questions:

1) Are there accounting apps (sort of like Quicken) available for Android or iOS (iPad/Apple)?
2) Can you run actual Quicken on a tablet?

For 1: Quicken (as far as I understand) doesn't run on Android or iOS but there may be accounting apps available for either. They probably aren't as complete or "connected" as Quicken. One way around this is using some sort of "remote desktop" program to access your PC (running Quicken) or using some web-based accounting program. If you need to move data to actual Quicken, you need to make sure that whatever you use can transfer data to actual Quicken.

For 2: To actually run Quicken, your tablet has to run a desktop operating system. At the moment, that means a tablet that runs Windows 8.1, like the Microsoft Surface Pro (not RT). There are other companies coming out with equivalent laptops. Given the price of these "real" Windows tablets, you might consider some sort of Windows "Ultrabook" laptop. (I have no idea if Quicken is available for Macintoshes. If it is, you could consider a Macintosh laptop too.)

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A table/laptop for touring means you want to strongly prefer something that is on the light and small side. Additionally, considering that you are in a "harsh" environment, you might want to avoid something that is overly expensive.

If you need a real keyboard, you might consider a small Bluetooth keyboard for a tablet.

Since you are talking about touring, you need to determine if you want a tablet that has GPS.

At the moment, the best tablet with respect to features and price (as far as I can tell) is the Nexus 7 (it has a GPS receiver). (Some of the Samsung tablets have a GPS receiver.)

The new "retina" iPad mini is very nice but significantly more money. If you want a GPS receiver, you have to get the cellular version (you don't need a cellular plan or a sim to use it).

Android is quite capable but iOS is more straight-forward (a bit easier to use).