It should go without saying that this is not an emergency. The Arizona state legislature looks like it will adjourn on May 23rd***, so there are 90 days from then for some planning. If the bill is not vetoed, the ACLU or another organization might sue to prevent the law from going into effect during that window, and a Court might issue a "stay" during the waiting period before the law goes into effect. I can't put any odds on any of this, since I am not a lawyer, I just know how to use a search engine, but don't freak out in an unhelpful way until we know for sure.
also we dont know what fully she signed or vetoed today yet. in fact a couple minutes ago aparently a news station was joking about not knowing what is signed or vetoed yet today and were wondering if she is gonna try and break last years veto record.