Right, my Girlfriend decided she wants to try Ladder Slasher with me

So, she would need to create her own D2jsp account which would also show on my IP address since we live together. I need an okay from the mods please. Also, if there are any special rules or what not that go with it (such as no transfering fg, giving fg etc.)

You don't need ok from anyone.
The rules are clear:
We allow one account per person. Be sure that anyone else using d2jsp in your household follows all site rules, and does not scam, or you could be held liable for any and all things they do wrong (and vice versa).