The first few nights are usually difficult on your puppy (and you!). Set yourself and your puppy up for success with these tips. The two hours before bedtime are very important. No food or water for those two hours before bedtime. Try and keep her busy or let her play for those hours before bed as well so that she'll be worn out. Make sure your puppy has been able to check out her crate (if you are using one) before she's put in it for the night. It's great to leave it accessible to her during the day so she can inspect it a bit. If possible, place her food and water near her crate so she will have to go near it and grow more comfortable with it a few times a day.
Your puppy will most likely miss her mom and litter mates. You will be the new dominant alpha "dog" in her life. To help with this transition you can set your puppy's bed or crate right next to your bed those first few nights. That way your puppy will hear and smell you in the night. This can be comforting for her. If she whines in the night you can tell her a quick "no" or "shhh" and if she continues give her a quick jerk on the leash or tap on the crate. Never too hard or scary. Don't pet her to "soothe" her as this will encourage her behavior and the whining will continue. And don't talk to her unless to say "no" or "shhh". She will learn that if she whines and you try to soothe her that this is a desired outcome and she will continue to do it.
Your Maltipoo puppy will most likely need to eliminate during the night. A potty training routine will help a lot to make nighttime and house training much easier. To make this as easy as possible, have her leash, a flashlight, trash bag or whatever else you'll need by your bed to make your trip as quick as can be. Your puppy should be able to last about the same number of hours as she is months old (and usually a bit longer during the night). So if your puppy is 2 months old she should be able to hold her bladder for 2 hours, 3 months old for 3 hours, etc. It's easiest if she is in your room or close to you so you can hear her when she needs to go. But if she isn't within ear shot or you're a sound sleeper you may need to set an alarm 5-7 hours after her last trip to the bathroom so that you can get her outside. Some puppies can hold their bladder all night, but not all can do that. When you get up with her, take her out quietly on her leash to the designated bathroom area. Keep your trip short and quiet. Tell her to go potty or whatever your cue words are and praise her briefly. If you get too excited over her in the night, it will turn into a "party" for her and this will encourage her to repeat it. Once she has eliminated bring her back to her crate or bed to go back to sleep. In the morning take her out first thing before you do anything else to diminish chances of having an accident.