OP you are NOT being unreasonable to feel anxious about this! You have a right to enjoy peace and quiet in your home.
Sadly many people think its ok to inflict constant noise on neighbours.
I recently moved out of my flat because of a very noisy out-of-control toddler next door. The constant screaming, shouting, banging walls, tantruming and running all night on hardwood floors made my life hell. I was being woken several times a night and in the day I couldn't relax, study or concentrate. My nerves were in shreds. I felt my only option was to move, I now live in a detached house and life is so much better!
Hopefully your neighbours won't be like mine. I suggest you give it a couple of weeks to let the child adjust to new environment and try to get on good terms with the mum. She'll be more willing to minimise noise of you have a rapport.
But also be firm from the start about what you expect! If the toddler starts waking you/your daughter every night, or causes other unreasonable noise, tell your neighbour immediately. And complain to landlord if it doesn't improve, as most tenancy agreements have a clause about not disturbing neighbours. Some specify 'quiet hours' usually 11pm-7am.
I firmly believe people with small children should NOT live in flats with poor soundproofing, unless they're prepared to make every effort to keep their child from disturbing others.