The rule is this:
If you think what you are reporting is not still true, you must backshift. But if you think what you are reporting is still true, you can (but don't have to) retain the present tense.
Me to Kate: "Where are you going?"
Kate: "I'm going to the cinema."
In this example, you are asking what Kate is doing right now, at the moment of speaking.
When you report this a week later, you must backshift if you think it is no longer true. Since "going to the cinema" usually takes minutes or hours (at most) to do, most of the time it is not still going to be true a week later. Thus, in this case, you would backshift:
She said she was going to the cinema.
However, if you think that the event is still true when you report it a week later, you can (but are not required) to retain the present tense:
She said she is going to the cinema.
It doesn't matter why you think this is still true, but if you do, you can use the present tense. And in the case of someone on the way to the cinema, it's not likely that a week later you would think Kate was still on her way to the cinema; but I am just answering your question using your dialog and time frame.
You know that Kate was going to a cinema that takes more than a week to get to. I know this is unlikely, but perhaps she was on her way to a foreign city and the main thing she wanted to do there was go to that city's world famous cinema. She could certainly report her trip as "going to the cinema." And it would still be true if you knew she had not gotten there yet but was still on her way. Maybe it takes 10 days to get to this foreign city. Maybe it takes 1 day, but the cinema was not scheduled to open until after she reached the city. Whatever the case, you can use is if you think what you are reporting is still true when you report it.
So, to answer the specific question:
Here, at the time of reporting after a week I don't know if she's still going to the cinema or not and even then I use 'is' will this be grammatically correct?
No, it will not be. It will only be grammatically correct if you know that she's still going to the cinema.