That was a sweet one-shot.  I noticed a number of spelling errors and a few run-on sentences that got a little confusing to read.  Aside from that, it was nicely written and not too rushed.

Nice concept but the asking her to be his mate part was OC. You have a good start on a chapter story where they could develop a relationship over time. Also, you had some spelling errors. Maybe a beta would help.

The idea is good.  Kagome has decided that she has no place in Feudal Era with her friends, now that Naraku has been defeated and everyone has paired up.  You've got the basis for great story.  The problem is that the story needs more development, especially the romance between Sesshoumaru and Kagome.  The background you've given so far doesn't support a relationship deep enough for mating.  However, there is enough information to advocate the beginning something more substantial between them.  

I'd also suggest getting a beta.  It's really hard as an author to catch all the grammatical and spelling mistakes.  There were quite a few in your story but it is easily remedied with some editing.

I hope you come back to this story and expand it.  I'd like to see where it would go.

There were some very nice points to this story, but first, to address a few flaws. You had some major spelling and usage issues here, and I would HIGHLY recommend a beta. They can help with those kinds of issues, but also, spellcheck will catch a lot of them as well. I think that if this story were fleshed out a bit, making it into a chapter story instead of a oneshot, there would definately be some serious potential. I wonder how a human Inuyasha would deal with his new life, how Sesshoumaru would really come to terms with his brother giving away the gift of youki from his father. How Kagome would agonize over where her real place should be. I think you could come up with some good ideas from what you started with. I think that sometimes, people get in a hurry to be finished instead of understanding that in most things, the joy is in the journey. While no one really likes unfinished fanfics, more time can lead to bigger payoffs in the end, right?

Sorry for rambling ^^;

it was an interesting concept, however you had many spelling errors throughout it and the flow was a little rough, however a little tweaking and i believe youll have a very good story goin for ya.

It had a great beginning but the spelling and punctuation errors made it a little hard on the word flow. The scene with Sess and Kagome happened way too quickly for it to truly be believable considering you never explained whether they had a chance to become friends or anything more before that incident. As flighty as Kagome can be, she would never just jump into Sess's arms just because he asked her to be his mate. And Sess would have faster proposed that "he needed her" to stay and that he possibly cared for her (even that's a lil OOC for him) before he would come out and say I love you.

As there are quite a few spelling and grammer errors, I'd recomend finding a beta.  The story itself started out pretty decently, but the scene between Sesshoumaru and Kagome seemed too OOC and forced.  Without them having any history romantically, I can't really imagine either of them acting that way, or rushing into the idea of being mates.  Perhaps if he had just asked for her to stay for him, without confessing or asking her to be his mate, it would have come across much better.