Starting a new job whilst going into my second trimester

I’ve just signed a contract 1 week ago for a new job which I will start on 1st June. I am currently on gardening leave until then & have found out this week that I’m 4.5 weeks pregnant. I’m now worried as I have a 6 month probation period which will end on 1st December but the baby will be due on early November so I will be one month off from finishing my probation. Has anyone experienced something similar before? It is a junior role I am starting so I am worried that will either retract the offer straight away or not allow me to pass my 6 month probation. I want to be excited but I can’t with this hanging over me :(