Just be careful how many drinks you carry at a time. Take two trips if you need to. The last thing you want in pregnancy is any avoidable back pain.
I am a hairdresses but I was also bartending up until my 19th week. I didn't want to have a pregnant belly pouring shots. However I think it is totally fine to serve pregnant. I'm sure your tips will get better too!
i have no issues with a pregnant server. my sister in law is a server at a diner and she worked up to her due date with both pregnancies. if you can physically do the job, don't let anyone stop you!