The only time you move up a level (that I know of) is when you move up a class. Ie Private Lower 1 moving to Private Lower 2 on 1 year anniversary. Or 6 months after becoming Class 3 moving to Private Lower 2 on becoming Class 2, on the 1 year anniversary moving to Level 3.
The downside is if you are promoted and up classed, you usually receive the increment progression first, and then move to the next promotion band. Thus not gaining any benefit from the AIP.
I think in your case you will move to LCpl Higher 6.