when to get blood test?

STM here.

For my first pregnancy, my GP ordered a blood test right away (around 4 weeks) to confirm pregnancy and also did a really comprehensive blood test at the same time, to check overall health going into the pregnancy.

This time, I don't currently have a GP (looking for one but idk how it is elsewhere, in canada it's hard to find one accepting new patients!) but I have an endocrinologist that I see for thyroid issues. she sent me the requisition today to get a blood test (just confirming pregnancy and checking thyroid, not much else) but i'm only 11-12 dpo right now.

endocrinologist didn't specify when to get the blood test, and i don't have an easy way to contact her for questions, i'd have to wait weeks to see her.

should i do it right away or wait to miss my period in the next few days then do it? or maybe wait an extra week after that? does it matter?