I'm surprised if you can move apps to SD at all with 4.0.4, as it's not supported by Android in that version (though some manufacturers add it).
No, just rooting by itself won't do this. Upgrades are device-specific, so you won't be able to upgrade to 4.2, 4.4 or 5 unless either the manufacturer has produced an upgrade for it or someone has built a custom ROM for the device (the latter requires root). Even then, it's unlikely that this will unify the partitions: generally manufacturers don't change that sort of thing when they write updates. For what it's worth unified storage came in with Android 4.0 (actually with 3 if you have a tablet), but some budget manufacturers stuck with the old way, which I guess is the case here.
If you were rooted there are various tricks that could be tried. The simplest is probably to partition a removable SD card and use an app called Link2SD to move parts of the apps to that: it allows you to move more than the built-in "move to SD" did, so should give you more space than that would, possibly more than unified storage would since an extra 2.2 GB isn't very much either. It might be worth checking whether it is already rooted - off-brand devices sometimes are (try a root checker app from the Play Store to see).