If it hurts your feelings for her to say, "you can go or you can stay, both will be fine by me" a wishy/washy non-statement of what she feels and so now she's worried you'll be/get depressed, that's her expressing her feelings, which is truly a good place you two have gotten to, congratulations!

But you can't have it both ways, with her telling you her fears (yes they're her fears but she's entitled to them!), and discounting what they "say". It is her family and her trip and that doesn't really have/say anything to do with you. She has her relationship with her family that she has had since long before she met you and it is only hers, just like your relationship with your nuclear family is yours, good or bad and you get to say how you relate to them.

Whether or not you would get depressed is not the question; she is afraid you might (and, you, in fact, might/might not) and does not think SHE could cope with her family and helping/loving you. You can't "argue" about what she feels, she can't help what she feels anymore than you can help being depressed. It's her family, she truly gets 100% say in how she/anyone "outside" gets to relate to them.

I would support her going on this trip alone. Maybe tell her she can call you whenever she wants/feels the need to but that you won't call her, will assume she's doing fine. Tell her to give your "hey" to anyone you especially liked or who especially liked you, etc.