It sounds as though you were using the threat of calling the police as an emotional tactic to scare your DP into getting your own way in the argument because you were intoxicated and out of control. It backfired with huge consequences. You may as well be honest, is this usual behaviour for you? Your child is not by a long stretch in a safe environment under the circumstances that you have given us.
As PP have said, it’s not normal to be drinking so heavily when you have a child in the house. If you and your partner were both drinking all night then that is an extremely serious safeguarding issue by itself without the domestic violence. It sounds as though your partner may not be an appropriate adult if he was also drinking and he’s smashed his phone and lied and said it was you. Are you sure it wasn’t you but you just can’t remember doing it or is he prone to telling lies about you? Either way it’s not good at all.
Alcohol is a depressant, it slows down your reactions in the event of an emergency and often goes hand in hand with neglect because you lose the ability to appropriately and safely care for your child whilst intoxicated. It makes people’s moods and behaviour irrational and unpredictable. Your child is extremely young and is fully dependent on you.
Your partner may be told by social services to leave you because the abuse you perpetrated was not only against your child’s other parent but in the presence of your child which as others have stated is child abuse. That’s if he can prove he’s a responsible adult himself. They may only allow you supervised visits with your child and they could end up making you take regular alcohol and drugs tests to ensure you’re not using. Where is your daughter now? If you’re both deemed a safeguarding risk to you daughter then she could end up in foster care until you can prove you’re able to care for her.
You are going to have to jump through as many hoops as social services deem necessary. That means you must stop drinking and any substance use. Your house must be clean and free from trip hazards and fire hazards. You must show that you can offer your child routine, that means regular meals at an appropriate time, clean clothes, adequate bedtime and bath time routines, your child regularly attending nursery.
Engage in any counselling or courses they may offer you, relationship and alcohol/substance abuse. You need to seek help for any anger or control issues that you may have and you need to provide a loving and emotionally stable home for your child. If your relationship is toxic then you need to leave it if you cannot provide a healthy environment living with your partner for the sake of your child’s emotional wellbeing.