What you are looking for is unity scope or lens. From my searches online so far I have not found a scope or lens that would allow searching for software.
However, if you are looking for an alternative to Software Center, I recommend you get familiar with lubuntu software center or
apt-cache search command in terminal. In the last year and half I've only used
apt-cache search some-app-name to search software and
apt-get install app-name to install.
If you want something graphical, I've put together a simple script that will allow you to search for software graphically. You can bind this script to a shortcut, such as CtrlAltI
# Author : Serg Kolo
# Date: Wed Jun 3 09:50 2015
# Description: list available packages graphically
# using apt-cache search and zenity
SEARCHTERM="$(zenity --entry --text='Enter key to search' )"
if [ $? -eq 0 ]; then
apt-cache search "$SEARCHTERM" | nl > $FILE
zenity --text-info --filename=$FILE