Indeed: 1s2 2s2 2p6 3s2 3p1
the first (13th) electron to go is the lone 3p electron.
After this: Al+: 1s2 2s2 2p6 3s2
The 12th is a 3s electron, not just one electron lower, but a full electron shell lower. This means it is a lot tighter attracted to the core and thus the huge increase in ionization energy.