[Eternal]

Wait, you've only been dating a week but you're already saying you love each other? It sounds like you're rushing things.
It could help if you took some time to really get to know each other. That might help you figure out if you do have a connection or not. If you don't, it's probably best to move on because it's likely you'd grow apart eventually. Her friends and cousin said that because they love her and don't want to see her hurt, but I'm sure they'd understand if you broke up with her gently and not just to hurt her. They can't possibly think you two will last forever.
Basically, do what you think feels right. If you think there could be a girl out there whom you'd work better with or be happier with, then go ahead and end things. If you want to wait a little bit and see if you get more interested in your relationship, then stay with her. It's your decision really.
I definitely think you should try and find a day which you can spend with her so you can just talk and see how things go. It's not really a relationship if you can't see each other and only text.