What can I add? Dooin is completely right.
Reputable rescue will assess, neuter, vaccinate, microchip, provide a full support and back up service, homecheck - which is for YOUR benefit as much as the dog's - and be insistant on taking the dog back should you ever not be able to keep him.
True, there are lots which have blanket policies and which will not rehome to families with young children, but there are others which will consider each application individually. Your best bet in this respect is an independent smaller rescue rather than the RSPCA/Wood Green etc.
And yes, this whole thing about alll rescue dogs having no history and a pup being better is absolute bollocks! There are NO guarantees with a pup whereas a rescue dog may well indeed have come from a family home and be in rescue through no fault of his own.
Let me tell you a secret too - when an owner comes to rescue with a dog which he says is perfect in every way but which he can't keep because he has to move/is ill/whatever, we don't believe him! This is because people lie... so we carry out our own assessments first, before considering allowing a family to adopt that dog.
Blunty, I would put it this way: if you can promise me that you will seperate your child and dog, if you can guarantee that you won't shriek "killer dog, put him to sleep!" because your child has pulled the dog's ear and the dog growled, if you can find time for your dog as well as your child, if you will train your child as much as your dog - e.g. not to disturb the dog while he's sleeping, not to touch the dog's food or disturb him while he is eating, not to think it's cute and acceptable that Johnny climbs all over Rover, that you will cope with a settling in period, maybe a dog which needs housetraining or lead training and be able to do that and be a mum... in anotherwords, you won't give up on that dog an I won't in time be seeking a rescue place for him or imploring you not to have him killed, go for it!