1.5 is an "alpha" (that "alpha" or "a" after the name meens it is a test version) with which developers and other PPL that use K-Meleon for a long time test future developments. That is done after the developers tested it alone. They need feeback from PPL with other surfing habbits, Windows settings ...
1.5alpha is AFAIK not compatible with all aspects of Your 1.1.2.
1.1.3 is an updated and corrected 1.1/1.1.2. It also has a newer Gecko Rendering Engine. It even has a newer engine than the 1.5a. So why change versions?
If You feel insecure You best create a backup of Your Profile ( You copy the profile to a save place - e.g. the whole folder to my data). You will find the used profile via Edit > Configuration > Profile Folder.
And also copy Your current K-Meleon folder also to a save place. That way You only have to copy both folders back to its old places and all works again like it does now.
Normally nothing goes wrong during setup so the backup is just in case.
To install any K-Meleon and the Loader (if You use it) must be shut down.
K-Meleon 1.1.3 is a complete browser with all the needed files (like 1.1).
For the actual setup You are offered to install into Your current K-Meleons folder
but You can choose another name and location. You could combine that other name with unselecting Multiple User Profiles. This gives You an install that is totally independent (especially of Your old Profiles and its user data) and it has its Profiles in its own K-Meleon folder / You need writing rights were You install it that way [ BTW: This is the way the old timers install their alphas
] .
You can also install 1.1.3 in the default location (Your Programs Files/K-Meleon) without deselecting the Multiple Profiles option. You probably installed 1.1 that way.
K-Meleon 1.1.3 is perfectly capable, compatible and save to use all Your old data from 1.1/1.1.2 in Your old profiles when You choose this setup.
Known problems: You have to reinstall some plugins and
extensions..
The installer deletes two folders completely
It is actually a bug in the extension installers which should not install in a folder that must be updated ;-)
If by chance You had deselected Mutiple User Profiles when You installed 1.1 just drop a file with the name of profile.ini into the install directory of Your K-Meleon. The presence of a file with that name will cause K-Meleon to use Profiles in its install folder.
If my explanation is not sufficient feel free to ask.
All here will try to help You.