I'm making a new character and she is a Wood Elf rogue. The rogue gets to choose two skills that she is proficient in at level one and give themselves expertise in it instead. A Wood Elf has access to the Aereni Expertise trait which is described like this: "Choose one skill or tool proficiency. Your proficiency bonus is doubled for ability checks that use it." Does that mean if I choose perception (a skill that I already have expertise in) would I then get quadruple the bonus?
No, you never double your proficiency bonus more than once.
If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.
The racial and class abilities both allow you to double your bonus, so you get to do that, but you can't double it twice.