With an engineering degree and an appropriate PGCE you'll never be unemployed, but (judging by regular conversations with my Brother who has a physics degree and PGCE and teaches secondary Physics) you'll also never be rich or unstressed. Also the time he spends at home marking, preparing lessons, etc. is at-least as great as the time I spend working - the short hours bit is all balls (but yes, he does get a huge summer holiday).
If you've recently graduated in Aero-Eng I'd recomend trying initially to work for a couple of years in the field. The understanding will stand you in good stead if you choose to go pilot (either as well or instead). But also, if you don't consolidate your degree with some real engineering experience then within a couple of years you'll have lost much of what you've learned and will probably struggle ever to get it back (or to convince any Engineering employer that you've a clue about engineering any more).
Incidentally the big aerospace companies (BAE, WHL etc.) are both the hardest to get into, and also the environments where you'll learn least since they'll stream you very quickly into a narrow specialist (do you really want to be a check-stressman?). I'd suggest looking at the smallest aerospace companies for employment.
And teaching is probably the only technical-graduate profession with less respect and poorer pay than engineering !
G