My sister is pregnant and her HR person says that they do not send out FMLA paperwork until 1 month prior to delivery. It was my understanding that she could take FMLA for doctors appointments. Can the employer wait until the last minute to send the paperwork out?

Has she ASKED to take FMLA to go to the doctor?

Yes, they just give her the time off.

Then I wouldn't argue it. Technically doctor's appointments are covered under FMLA but if her employer isn't requiring her to document it as such and isn't tracking it to count against the 12 weeks, I wouldn't worry about it. That's more time she has after the birth. Usually I get protests for counting the time as FMLA. I've never had anyone complain about not counting it as they then get more time after the birth.

Technically yes, it is a violation but no harm, no foul. The employer can always choose to be more generous and allow 12 weeks after the baby is born, just not less so.