Hi Kate,
Firstly Congratulations on your pregnancy!

I personally would not tell them but maybe it would depend on the job you are applying for iykwim? Are you planning on goin back there after bub is born?
When I fell pg last year I had to quit work as I was passing out and vomiting (not a good look for a waitress lol) then when I came good around 13 weeks I got a job in retail. I didnt tell them I was pg untill I had been there for 3 weeks and then I pretended Id only just found out. I felt SO bad lying but I didnt want being pg affect my chances getting the job I wanted and ultimately I had to worry about the bills getting payed not the feelings of a company.
They were all stoked when I told them and no hard feelings when I left.
Best of luck with whatever you decide to do