Hello, I am Dr. Peter a licensed Veterinarian. I would like to help. I need to ask you a few questions to be well informed and give you the best advise. There is no additional charge for information request.
1- Are you currently feeding the cat in a specific place and time?
In response to your question, a cat without any food can go for weeks without dying. Certainly, that will depend on the health status and fat. But, overall they can go for at least 2-3 weeks without any food. Outdoor cats (strays) usually are very good hunters and tend to eat mice, rats, birds, squirrels, etc. I think she will be fine during your week of vacation. But, what you can do is buy an automatic feeder and she will have her daily food as you have been feeding her. You can find automatic feeders in any pet store. If you follow the link below it will direct you to a site where you see automatic feeders.
Hope the above helps, if you have additional questions I will be glad to answer them.