Flu shots are not recommended for pregnant women in their first trimester. From the Govt website

Immunise - 2.3.2 Vaccination of women planning pregnancy, pregnant or breastfeeding women, and preterm infants

(ii) Pregnancy

Although the use of most vaccines during pregnancy is not usually recommended on precautionary grounds, there is no convincing evidence that pregnancy should be an absolute contraindication to the use of any vaccine, particularly inactivated vaccines. The only exception is vaccinia virus (smallpox vaccination), which has been shown to cause fetal malformation. There is some evidence, however, that fever per se is teratogenic.1,2 With the exception of the use of influenza vaccine, the NHMRC takes the conservative position that the use of vaccines during pregnancy might cause fever and should be avoided other than in situations of increased risk, where the benefits of protection from vaccination outweigh the risks. Eliminating the risk of exposure to vaccine-preventable diseases during pregnancy (eg. by changing travel plans, avoiding high-risk behaviours or occupational exposures) is an alternative to vaccination.

Live attenuated vaccines are contraindicated for pregnant women because of the hypothetical risk of harm to the fetus should transmission occur. If a live attenuated vaccine is inadvertently given to a pregnant woman, or if a woman becomes pregnant within 4 weeks of vaccination, she should be counselled about the potential transmission, albeit extremely unlikely, to the fetus. There is, however, no indication to consider termination of a pregnancy in this situation. The following table may be used as a guide to the recommended use of vaccinations in pregnancy. Information regarding pregnancy status in women of reproductive age should be part of the routine pre-vaccination screening checklist (see Section 1.3.4, Pre-vaccination screening).

-----They're giving free flu shots at work, but they warn you that pregnant women in their first trimester should not have the vaccination.