Are subsidized daycares in quebec obliged by law to give equal opportunities to everyone?

Not likely legal but it would be easy for the daycare to give the government a reason why she was moved ahead of you on the list. Rather than fighting about this, enlist your friend to help you get in, too. Bring over a plate of cookies and ask her for help in getting in. You will get nowhere complaining or even turning in the situation to the government. In fact, you may find you are never called.