Dear Aunt TUAW,
I've searched your site for information on this to no avail, and I suspect several others will be faced with the same dilemma. Seeing that you are the authority in the field, I thought I'd ask you. Here goes...
I've recently sold off my iPad 1 on the used market in favor of getting the iPad 2. Prior to selling it, I applied the iOS 4.3 update and performed a full backup on the device using iTunes. And so to my question:
Will I be able to perform a restore by use of my [iPad 1, iOS 4.3] backup onto my new iPad 2 in order to smoothly get all my settings and apps up and running on the new device?
Your nephew Jimmy
The first time you connect your new iPad to iTunes, you'll be given the option to restore from a previous backup from the same device class or to establish a new device. Using backup data allows you to restore a new iPhone to the state of your previous unit, or in this case, your new iPad to your old one. If you opt not to restore this way, you can change your mind later by using a simple iTunes feature.
Select a device from the sources list on the left side of the iTunes screen and right-click (or control-click) that device name. Choose "Restore from Backup..." from the contextual menu then choose a backup to restore from via the pop-up menu. Be aware that device backups from 4.3 installs (like you have) cannot be restored to devices running pre-4.3 software (although you can use a partial workaround if needed).
You can select which device backup you want to restore from, as well as which backup (they are dated) you desire. Then just click Restore and let iTunes do its thing, which usually takes about 10-30 minutes to perform, depending on the amount of data you need to restore.
For best results, make sure to back up your device regularly. You can choose "Back Up" from the same contextual menu to manually do so. Synchronizing your device to iTunes will automatically back up your device as well, unless you've changed the iTunes defaults.
You can manage your backups by opening iTunes > Preferences... (Command-,) > Devices. Here you'll find a list of individual device backups. To delete one, select it from the list and click Delete Backup.
For more details about backing up, restoring and updating your iOS devices, check out this Apple knowledge base support page.