does she want to have a relationship?

Im australian and Ive met a japanese girl here in australia while she is studying. Im really interested in having a long term relationship if possible. We have been to dinner twice and seen each other maybe twice a week for the last month and im very keen on her and she seems happy with me. I have romantically spoken to her and told her Im in love with her. She proceded to say japanese men only say that they like them the but its ok for me to say 'ishiteru'. Reading all the threads im confused if it is just friendship.
Now, we have kissed and cuddled each other but 2 things puzzle me. How do I ask a japanese girl if she wants to be my girlfriend? And if I want to ask for a long term relationship ie leading to engagement etc what do you normally do in japanese culture?
One thing I know is she is going to japan in 3 months time to visit parents but she said she will be back.
Lastly what also puzzles me if I text her it takes her 2 or 3 days to reply. Why do they leave it so long?

Do you really thing there's a certain way to ask a girl to be your girlfriend? Not all Japanese girls are the same!
Just freakin' ask her!

Thanks, I know all women are different and its up to the individual persons involved how to ask if they want a steady relationship. However if I wanted to indicate to her that I want more than just bf gf is there a traditional way in japanese culture to demonstrate this? She is still learning english but still misinterprets some things I say and gets confused!

The traditional Japanese way is to clearly ask her that you and her both want to be male/female relationship, so you need to ask her "Will you be my girlfriend?", I don't recommend you to say "Do you want to be my girlfriend?" even though it can be accepted to say in Australia.

She may find still unsure about you therefore she may respond you. I don't know.

so funny.
"Will you be my girlfriend?" or "Do you want to be my girlfriend?"
in both sentences, you look down her, when they are translated into Japanese.

you may say
May(Can) I be(become) your boyfriend ?
I don't know you feel it strange. but, if translated, it sounds very good in Japanese.

Thankyou tokyo friend 88. I will ask her the way you say. Thankyou for your advice.
Im hopeing all goes well.!

You know, if you are already kissing and cuddling and she has told you it is OK for you to say "aishiteiru" to you, I have some good news for you: You are already her boyfriend; she is your girlfriend. If you ask her to be your girlfriend now, it is going to seem ... odd/weak. Instead, act as if you are her boyfriend, and you will be.

Just the fact that in the midst of you declaring your love for her she took the time to explain to you that Japanese men say "sukidayo" but also say that it was OK for you to use "aishiteiru," presumably because you are a foreigner and it sounds more romantic/exotic to her, tells me she is a very confident and composed woman who is comfortable with the idea of a foreign boyfriend, so that further makes me think an awkward request to be her boyfriend is going to strike the wrong note.

You aren't Japanese, and she probably doesn't expect you to be Japanese in behavior. The fact she is studying overseas and dating you (a foreigner) makes her not a "typical Japanese," whatever that is. So just use your common sense and deal with her as an individual, not as a "Japanese girl."

Don't ask for a long-term relationship heading towards engagement, either. It either happens or it doesn't. At some time a little further down the road, you might discuss the possibilities for the future, just to make sure you are both on the same page, but not after just a month of dating.

In any case, a long term relationship is not something you ask for and she grants to you. I'm pretty sure you already know that, but your question kind of sounds like you think that is something that is done.

Good luck. Also, don't fret about the 2 or 3 day lag before she responds to your messages. She may be busy (she is in your country to study, maybe she takes that seriously), and if you bring it up it is going to sound desperate and clingy,

Thanks Dan I appreciate your comments. I feel I am a somewhat of boyfriend to her already and from what you have mentioned makes me feel a little more confident of this situation. I work full time and she currently is in queensland visiting friends for a week and its the anxiousness of her not replying to my text that just somewhat worries me. Although I suppose there could be other reasons like' she lost her phone'.
I know she'll be back next week so I think ill progress from there. I know she appreciates my comments to her. Every time I see her I mention how beautiful she looks. ( im a bit of a romantic at heart) and after a few dates she has even said to me that since I made those comments she feels more confident the way she physically looks. She seems to be a very down to earth girl not materialistic and thats one thing thats attracted me to her as well as her other traits. :).
Anyhow ill see how it goes next week.
Thanks again.

why don't you call her instead of waiting days for her to reply?

I dont know why really. Shes always asked me to text. She has a japanese phone brand and I just assumed she cant take calls but only text.
When she went to queensland she said to me you can text me while im there!. Or maybe she feels like she might not understand when I talk over the phone thats why she asked me to text.
When we are together I talk slowly and if she dosent understand I sort of use actions to express what im trying to say. You see I can tell from the expression on her face if she dosent quite understand so its easier for me and her if we are face to face.

Sorry dude.. sounds to me like she is just after a little local fling while away from home. Girls are no different to guys. The reason she is not replying is because she is "busy" with someone else. Holiday time is fun time! She's happy while with you but the eyes start wandering once away from you looking for her next conquest. Why would she reply to your calls or texts, it seems like you can both hardly communicate when together anyway...let alone when you are thousands of miles apart... move on with your life IMO