What is currently making you think it would be good to live together after just a year?
What would be better for you and your child compared to the current situation?
All that is coming across just now is massive negatives.
I don't think it sounds like a good idea at all.
Dp and I decided to move in together after about 4 years, I think. My children knew her fairly well by then. We had all had lots of holidays together. We knew we had compatible approaches to finances etc. It took us another year to buy somewhere together.
Neither of us could have bought a place alone.
Even after 5 years it felt like quite a big decision and I did worry about the children adjusting.
You just sound OK as you are. You like your job. You are on the way to property ownership. That would mean an inheritance for your dd, potentially.
An alternative scenario might be:
You keep saving up for a house.
You buy it and move in with your child.
She stays in it and pays you rent equivalent to 3/4 of mortgage (or whatever is fair) so she doesn't have to move in with this guy if she doesn't want to.
You move in with him and use your income to keep paying maintenance on your property.
You stay full time because you enjoy your job.
It can be hard to work out what should happen in a healthy relationship but one key thing is that there is compromise and that you feel confident to speak out if something will disadvantage you.