If you're in the United States, labor laws prevent companies from using discriminatory hiring practices and also prevent companies from taking later discriminatory action on employees as well.
This includes 'disabled' people and this further includes people who manage chronic health conditions.
It also enforces a 'don't ask don't tell' policy when and if an employee is disabled and/or manages a medical condition which may need treatment during the course of their work term.
The HR manager/staff will need to know and this information IN ITS MOST BASIC FORM (literally, this employee manages a chronic medical condition) - may be passed down to the employee's manager (the employee is more often than not given the choice to further disclose to their manager or not)... but this information is otherwise completely confidential and is partly related to HIPAA laws regarding the privacy of health-related information.
That said, it is NOT your business in any way, shape, or form.
It's great that your male co-workers can spill the beans on the whys and wherefores, but not everyone (and NO, this is NOT a women-only issue) is willing to do so for a variety of reasons including the possibility of being further discriminated against.
If your company is willing to keep her on staff because despite her need for accommodations, she is still qualified, then the company needs to also know that accommodating her may equate to rebalancing the work load by adding extra help, extending deadlines at times, etc.
(Edit - 06.09.14: The next three blocks of text were added to elaborate on my response specifically regarding the OP's issue/concern re: shouldering the additional workload at the behest of their manager and addressing that specific concern as opposed to 'how do I deal with this particular co-worker' because of that concern.)
No two workplaces are alike and if your manager is wanting you to do some extra work, then that is your manager's prerogative AND perhaps an issue to take up with your manager once more OR escalate to -their- manager if you feel you are being unfairly or wrongly treated or discriminated against, etc.
HOWEVER, you would NOT address this issue in the way you asked this question by blaming another employee and what you see to be potentially suspicious health-related absences. It is inappropriate and also an invasion of another person's right to privacy regarding personal matters and could get you 'dinged'/monitored for harassment/discrimination against that employee... especially if she complains about your confrontation(s) with her.
Monitor your workload and your team's workload and the rate at which things are getting done and if you and the team are struggling to get things done according to the timeline the manager has set, then present the problem factually and logically as it is and without playing the blame game.
This is a COMPANY issue, a COMPANY RESPONSIBILITY issue, a MANAGEMENT issue, a MANAGER RESPONSIBLITY issue.
It is NOT a WOMEN issue or even a CO-WORKER issue and additionally, by CONFRONTING ANY co-worker on their 'medical issues', you open yourself up for a harassment case filed against you.
What your co-worker's situation is is a PRIVATE one and the people to address it isn't fellow co-workers.
And no, your co-worker is under no obligation whatsoever to provide YOU or anyone else who is NOT HR/management a doctor's note.