What are your thoughts on this? Don’t know if I’m overthinking or being sensitive. 

It’s a dealbreaker OP. You will find someone else.

Big red flags. Stop having her around near your daughter. The “she knows what she’s doing” is pretty scary TBH. Let alone the general crapness/ defensiveness.

She is assuming bad motives of your daughter, as if your daughter is trying to annoy you or being manipulative.

Imagine what it would be like for your child if that continues? Just being herself, in her own home, she'd be accused of deliberately causing difficulties when she is only being a 3 year old.

Has your DP ever shown love towards your child?

Put your child first and get rid of this woman.

She sounds like she could be a little unhinged! A bit Jekyll and Hyde!

I wouldn't trust her with my child.

I've watched too many crime things were the new partner starts of with lunacy like this, it never ends well.
Back in the day, I was the youngest in the family, hadn't ever been around kids as an adult. When I met my first partner's niece, I absolutely loved her immediately, as in, it felt natural to play and to make her happy. Because she was just a child, not to impress anyone.
I wouldn't ever be in a relationship where someone was putting my child down and putting malicious motives on their innocent ways.

Please end this relationship. She clearly doesn’t like children and she’s trying to put on an act with your daughter. It’s ok to not like children, but the relationship is going to work.

Eek, it certainly doesn’t bode well! Yet sometimes, speaking from experience, initial awkwardness can be smoothed out with a bit of time and getting to know your child better. Is your DD pretty average in her play etc? I know a friend with DC with demand avoidance who want to be in control all the time and it’s been hard with other people

Try thinking about it from your DD’s perspective.. how would you feel knowing she is also picking up on this ‘vibe’ from your partner, and her parent is brushing it off instead of prioritising her?

The fact you felt secure until she met your DD says it all, she was fine with you, not the full package. I wouldn’t have anyone in my child’s life who wasn’t adding to it. You already know the answer if you’re posting this.

It must be really hard to have built up your own relationship with her & now are trying to navigate how you all relate with the inclusion of your DD.
But I don’t think she’s prepared or able to “share” you with your DD & is trying to undermine your relationship with your DD. This is a huge red flag OP!! It’s time to separate from her. She’s sounding toxic & not suited to blended relationships or someone with DC. And she may have thought she would be, but really is not. It’s coming out in her criticising & undermining your relationship instead of enjoying & validating it. What she says about you being a mum & having a DD & how she’s acting around you both is showing you that. And I would not really want her around my DD. You know your gut is telling you that.

She is a total bitch , anyone who shows such meanness to an innocent 3 year old child needs ditching now , don't give her even one more chance ,she has shown her true self and if you continue with her your precious little girl will suffer, no two ways about it.
Please do not let this child become another statistic -life badly damaged, possibly ruined by its mother putting their partner before their child.
You get one chance only to give your child a happy childhood , one chance.

‘I’ll shortcut her to ‘DP’ for ease of reading’

You know when you hear stories of children who were abused and killed by their once-loving parent but turned on them when they were in a new relationship? This is what happens if you stay with her.
You need to leave or she will try and poison you against your daughter.

Why are you calling her DP? She’s a girlfriend until you move in together and actually get serious for a start. For another she clearly doesn’t like children. I like my own children but am not that keen on other people’s - never have been! And that’s absolutely fine but if you want a step mum substitute then I’d stop looking at this one!

You need to either bin her off entirely or keep her completely separate from.your DD and only see her when DD is not around. She doesn't like your child and I wouldn't allow her to be with her.

If i were you....?

My priority would be my child on that basis the options would be

A. Shag her when you do not have custody of your child but never cohabit, never plan to marry, never holiday or socialise with "D"P and child ie. no real future

B. Break up now.

This woman cannot signal more clearly to you how deeply unsuited to being a stepparent she will be.

If this is the honeymoon period I dread to think what an absolute shit show it will be if / when she gets pregnant and you have a child together... your poor daughter!

As a single mum to a child of a similar age myself, I couldn’t be with someone that’s like that with my child. Just think longer term if she’s around your daughter more, she will become more difficult and your daughter will eventually pick up on these odd behaviours and will feel like it’s her fault.
Also, 3 year olds aren’t manipulative and they certainly don’t say things intentionally to piss you off, such a weird thing to say! They push boundaries because they always want more play time, but they’re too young to be manipulative. Your partner really isn’t a natural with children, and her not having children herself doesn’t play a part in that. It’s just her personality.
It’s a shame it’s taken a year to find out, but you also done the right thing waiting. I’d seriously be considering whether to continue this as it’s not fair to your daughter to put her around someone that’s just doesn’t care to get to know her and treat her like the small sweet playful girl she is…

If that's what she said on first meetings imagine what she was thinking.

That line " she knows what she's doing " made my blood run cold . Not saying she would hurt Ur kid but I've wondered how partners ended up abusing their partners kids. That kind of jealousy is something to think about but for me she'd have to go id always feel on edge and be on the lookout .

She doesn’t seem very well suited to kids (which is, of course, her prerogative) and doesn’t seem to like yours. I’d end it on that basis. DD comes first before anyone and anything.

She’s not used to three year olds, resents the amount of time and energy your DD takes up, has no interest in playing role-play games, and has no particular interest in rectifying the situation. I don’t think it’s a goer, especially as you don’t sound terribly keen on your girlfriend yourself, OP.

This relationship would not work for me, she doesn't care about the most important thing in your life, this will impact on your DD's self esteem as she grows up.