I believe the word you are looking for is GLANG. You and your certain lady were GLANGED over the weekend, and your relationship’s substatus is now ENGLANGED.
You may refer to each other as “my GLANGIÁNCED,” or as the kids say these days, my “OLD GLANGER.”
I may be remembering it wrong, though. Congrats either way!
I don’t have a single word, but the phrase would be “off the market.”
Congrats!
The term is “infatuated.”
I don’t think I’m perfectly clear on the timeline of events in this particular case, however in general relationship terms:
– If you have both talked about marriage, and both agreed that you will be married at some point in the future (specific date or timeframe unnecessary), then you are engaged.
– If you are in a relationship and mutually working towards the ultimate goal that the relationship will lead to marriage (lifepartnership, LTR, or whatever similar term you like), but you have not yet committed yourselves that it will definitely happen, then you are in a serious relationship.
Baubles, jewelry, formal rituals, or bended knees are not required for either of these.
– If you or the other have no particular goals in mind for the relationship, it’s casual dating.
That’s a kind way to put it. I was thinking “deluded,” perhaps.
There is no way that one month is enough time to know what the OP thinks he knows. It might work out for him, but he’s a seriously lucky bastard if it does, because it’s a shot in awful dim light right now.
Old school, call it “Going Steady”.
Your romance is a whole 1 week old, and you’re already talking about some sort of formal commitment? Yeah, “infatuated” covers it. This is way, way, way too early to be planning a life together, my friend.
Meh. My husband came over on our third date and just never left. Sometimes when you know, you know.
OP - she’s your girlfriend. Your her boyfriend. If you are shacked up you can say that you’re shacked up.
No need to get all complicated. 
Oh - and congrats!
I’m all for “when you know you know.” However, wanting to define your relationship as more than just dating after one week is a little excessive under any circumstances. There’s that famous person rule too, the more you flaunt your relationship to the tabloids, talking about how “meant to be” you are and how you’re totally going to be together forever, the more likely you are to split within a year.
Not to piss on your cheerios or anything, OP, I think it’s great that you’re so happy. Just don’t be so anxious to define what you have as more serious than dating. At least wait a month 
How about the good old English term “betrothed”?
So let’s see if I understand this. You met a month ago, and that makes you “old friends”? That may be accurate if you are a one-year-old.
My partner and I met on a Friday night and spent the entire weekend together, and pretty much agreed that we had a future together. But I’m fairly certain that it was more than a month later that we considered ourselves “old friends.”
Claiming you’ve met your soul mate after dating a week is a mark of immaturity. Are you very young? If so, you’ll be surprised by how fickle love is. Your pain is going to be proportionate to the joy you’re feeling now.
“Getting the milk without buying the cow” is a charming old folksy phrase. 
“Happy” and “fun” is how I’d describe your situation. Who knows where it ends up from there? But enjoy it!
They should put double down that it will be over within another two weeks.
You are not “old friends.” You barely know this chick. She might end up being your soulmate, but you couldn’t possibly know that after dating her for a week. Have yiou ever had a girlfriend before? This sounds like a very immature and deluded response to a normal rush of infatuation. Here’s a head’s up – that infatuation is just endorphins. It’s brain chemistry high. It doesn’t last forever (though it can last a few months) and it isn’t love. Love takes a while.
The answer to your OP is that you have a new girlfriend who you feel good about. Congratulations. Seriously, congratulations. That’s nice. But that’s all it is. Everything else is just daydreaming and talking. You don’t have a special connection that you need a special word for. “Girlfriend” works fine (and even that might be a tad premature).
Betrothal is a formal engagement.
Dating two weeks…ready to move in with each other, and talking marriage.
Blinded is the word to describe you.
How old are you?
‘hopped up on dopamine’
But I’m not sure he’s even getting any milk yet, but he’s already reaching for his wallet.
I’m definately interested in hearing more about Scuba’s circumstances. Age, number of relationships, ect. Could shed some light on the situation.