To qualify for FMLA, ALL of the following have to be true. If even one is not, FMLA does not apply.
1.) The employer has to have no less than 50 employees within 75 miles of your location
2.) You have to have worked for this employer for no less than 12 months.
3.) In the twelve months immediately preceding, you have to have worked no less than 1,250 hours.
4.) The illness has to be a "serious health condition" as defined in the statute.
BTW, even if FMLA applies, a note from the doctor saying "Joe was seen in my office on xx/xx/xxxx" or even "Please excuse Sally from work for the following dates" is not enough. The employer needs to have enough information to determine whether or not FMLA applies.