lying about due date?

teaching until july and my contract will be renewed second week of september 2018 and i just found out I am pregnant. we do have a maternity leave policy that would make me HAVE TO not go back teaching from the 5th of sept. I have an appointment at obgyn and she will ask me about my first day of my last period. i thought about "lying" and say it was 1-2 weeks later than it actually was. this way,my due date would be calculated a little bit later and i would still get the chance to sign my work contract. otherwise I'd be unemployed. do you think it is wrong to say start of af happened later then it did? i mean, doctors also only guess about due dates..?