Hi Nae. As a pro-vaccer, I asked my parents and FIL to get the free booster. DH got one too and I got one a couple of days after she was born. They were all free (paid for by the NSW govt).
I would've asked SIL too except she'd already had whooping cough a couple of years ago.
I think your email to family members is a good idea.
To me, close regular contact would be the people who will be holding her on a fairly regular basis within the first 6 weeks - maybe weekly or a couple of times a week.