new hard drive installation

First, which version of Windows is this? If for pre Windows 8, yes Windows Easy Transfer (WET) is the tool that does this BUT I can't say anything about IDailyDairy. That is a program you seem most worried for, so I would make a MANUAL backup in your Documents folder, then yes WET will back that up as well.

The normal process would be get ext drive, run WET to ext drive, download and make DBAN CD, get out all other CDs or software (if you downloaded software, and have room on the ext. drive, good time to place a backup copy of the software on the ext drive as well to speed things up).

DBAN the HDD (to keep your privacy on it and to ensure you don't conflict with the new 1TB). Install new drive. Install Windows to new drive. Install all Windows updates and options EXCEPT BING. Download and user SlimDrivers to install the latest drivers. Goto Filehippo.com and download the latest Malwarebytes, and either AVG or AVAST (you may want to consider Panda also, I am still evaluating it personally but it is nearly 100% detection repeatedly by independent labs and is still free for the basic AV uses) and install them. Now install all your programs (you need the Malware and AV protetection just incase you weren't aware something was infected). Then run WET to recover your system.

Yes your wallpaper will be back, the icons, everything.

if all you are doing is replacing the hdd then use a cloning tool like macrium reflect or acronis tru image (there is a free version for wd hdds).you simply boot to the old drive and clone it to the new drive and voila,bobs your uncle.