What alarms me is the question "Who should she contact to collect unemployment?" Duh. If she doesn't have computer access to file unemployment at her official state of Florida website, she would need to go to a Workforce/Career Center that was run by the state. They'll have computers there she can use, or a telephone system available and will provide direction and guidance in how to get the claim filed. Her. You can't do it for her.
That said, the reason waitresses often do not qualify for benefits has more to do with several other things than the general "waitresses" classification.
In the first place, she must have been working for a state unemployment tax paying employer for the past 18 months (or several different employers, they would all show up on her social security number in the unemployment system) and have sufficient wages to set up a claim. Just because they take out social security does not mean they are covered by unemployment, though the two things do tend to correlate.
This would determine her montetary eligibility for benefits. If she doesn't have that, there's nothing else to determine, she just doesn't get benefits. But even if there is monetary eligibility, the weekly amount will probably be quite small, as waitressing does not usually lead to large earnings, and the maximum unemployment claim in Florida is not very big anyhow. Filing a claim and waiting many weeks to see if you qualify for less than $200 a week in benefits for a limited time may not be financially feasible.
Especially since by the nature of the work, waitressing jobs are around more than good long term manufacturing jobs. Service industry jobs are more prevalent, and she will need to be searching for equivalent jobs anyway, even if she was approved to draw benefits. Chances are that even in these times, she will be able to replace the job more quickly than she would ever be able to get unemployment started and appealed and through the system.
Then we get to the issue of the reason she was fired. In almost every company that has any sort of a handbook, a no call/no show absence is considered misconduct, even gross misconduct, which can mean you're fired after the first occurance and you likely won't get unemployment benefits approved. So this behavior probably hasn't happened before, because it usually doesn't warrant a second chance. All the chain and fast food places have this policy, no call/no show/no job.
There are a few circumstances where it might be different, for example if the person were hit by a bus while on her way to work and was in a coma when she should have called. But just "I couldn't get to a phone to call in cuz I was staying at my friend's apartment and I didn't get to charge my cell," is not going to work as an excuse. To receive unemployment you must be out of work through no fault of your own.
So her chances of being approved for unemployment aren't great, her benefit even if approved woudn't be very much a week, and it will take a long time to be approved if she is approved. That said, waitresses certainly should file for benefits if they are fired. It never hurts to file, it doesn't cost anything, and if it works out, she has gained.