Honesty is the best bet. Spend the time with them over the weekend then when you and partner are alone talk to him about it. Explain that whilst you accept that he has a child and you are enjoying and committed to the relationship you are in, that for you, that doesnt mean you have to rush to move in together and get married and become an "instant family".
Explain that yes, you are not used to being around kids that much and given the very nature of children, you can find their exuberance a little over bearing and feel that this way you both get the best of both worlds. He gets to enjoy time one to one with his daughter (which is ultimately the point of the visitation) and also quality adult time with you. Likewise you get to be around for the "fun" stuff as and when you wish to be, thus helping your relationship with SD to be built as a positive one. Whereas if you were to suddenly move in together, the stresses that come from that, along with the household rules that YOU would expect (if they are not in place) would cause tension and argument and you dont want that.

But also, its important for you to find out NOW what you both want from this relationship long term. If you are totally ok with basically living apart but being in a committed relationship then thats fine, but its not fair on him if hes got the stereotype of moving in, getting married and having the "normal" type relationship goals. You are both entitled to the types of relationships you want to have, but in doing so you have to accept the fact that your partner may turn out not to be suitable for you (or you for him) just the same as conversations about kids. If one wants a large family but the other wants to be child free, you cannot be surprised if eventually that becomes a break up issue.

Most importantly, listen to yourself. If you, even whilst in a positive place enjoying your relationship, can identify that moving in would be a bad move. Then dont do it. But make it clear to him where you stand and you have to be aware that it might not be ok for him.

Tell him you move in as soon as he buys a large duplex or a multyfamily house that has a big , fully self contained in law suite with a very sturdy DOOR that completely separates the living quarters .

That's how I live and it has saved my sanity and marriage !

Nope...Don't say a word to SO about SD. It will not go well. They don't want to hear about their crappy parenting or that the child they raised is horrible.
Just keep avoiding the topic of moving in together like you have been. Keep doing your own thing and do not cave.
There will be nothing but misery for you if you move in.
You need your kid-free space and hinestly I am a bt jealous. I wish I had my kidfree space when it was a kid weekend.
If you see the signs now that the SD is difficult, it will only get worse if you move in. NEVER better.

As long as he and ex parent sd the way they do and sd is the way she is we will never ever live together.
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Smart woman!!!

you're going to run out of excuses sooner or later. this man needs to know the truth. it could be a very badly needed wake up call for him, but if not NEXT. and then congratulate yourself for dodging a bullet.

Oh how I envy you--you are so smart. Btw, your bf wants you to move in because it would be "easier", that's a big red flag to me. Yep, easier for him... not for you, don't do it!

I think you could say you don't want to move in because of your reasons (a, b & c), and also because it wouldn't be in the best interest of his child. That if things don't work out, the child will not just endure one divorce but will be hurt when you two split. Tell him that getting a stepmother is most difficult for girls because they feel like they are betraying their own mother. Tell him you don't want to put his precious snowflake through this.

My hairdresser and her boyfriend live hours apart. They decided they would not move in together until both sets of kids are grown. The youngest was 9 when they started. BEST DECISION EVER, AND I'M SO JEALOUS.

They meetup together for romantic times. Sometimes they meet up with the kids. No drama, no power struggles.

What's interesting is that she knows that she dodged a bullet. Now that her BF's daughters are teenagers, they are SUPER possessive of her BF. They sometimes force him to get off the phone when he's chatting with her--even though they've had a great relationship with her. She's SOOO happy she doesn't have to live with this.