It is safe as in it won't do you any harm or the baby.

However, because the oils in your skin and therefore on your hair change during pregnancy you may find that any colour or perm that you use either doesn't take as well or takes stronger hold of your hair than you would otherwise have expected.

The best compromise is to use a temporary colour or use straightening plates or curling tongs on your hair (with appropriate hair protection).

Otherwise make sure the salon knows your are pregnant and have a sit down consultation with the stylist who will do your hair, and discuss your options and risks to your hair thoroughly first.