There are a few things to seriously consider. You are not in a hurry - take the time to really dig around and start thinking like a dog (if you don't speak a second language, it's time to learn canine). You had time to prepare for your child, now is the time to think dog.
Everyone is different - dogs are different - however if someone does not OK a dog with small children, accept it. As a very experienced dog owner - the age of your children has nothing to do with it.
It's all about your level of confidence, patience, adaptability, and compassion. I've had dogs all my life and if I showed you photos of 100+lbs 'babysitting'... or walking the kids.... The huge fella who attached himself to a 14 month old, head on shoulder sort of thing (still makes me tear up)
Dogs are very smart!!! You have to learn to oursmart them.
The six hour gap - definitely makes me think you need older - but the most important thing is to learn. Morning romp, evening romp, add training and this could be done.
Reasearch. Why a dog? I'm sure you've heard that most of us would be childless if we had waited for the right time - - you dog is going to need time from you and so is your child.
Can you handle two toddlers? How about four? If it has four legs it counts as two in my book and all two year old children seem to split and become two at times. They really don't call it the terrible twos for nothng and you also have time to get to know your child before solidifying the canine bonding process.
You have time - so understand that many rescue places cannot accept the liability and unless the dog has been fully evaluated and approved for toddlers, keep looking. Not all dogs are kidproof, that's why many are rescued. Not all dogs like kids and not all kids like dogs. Not all dogs are 10 and up only. If you are looking for a 1-2 year old dog, ask questions and then ask more. Sleep on it. Think about it.
Basic size differences between children and dogs can be a serious problem - depending on the dog, the child, etc. An exhuberhant dog who has no idea about anything behind his head can and will knock down a small child - or damage an adult person's knees - in larger breeds it takes longer for their brain to sometimes catch up with their actual size. Watch dogs at the dog park, anything over thirty pounds under the age of three probaly has no idea where it's butt is going once the tail starts wagging. Small children move quickly, can make loud sudden noises, forget things a lot because they are basically in training themselves. Not all dogs can handle that - so from a rescue perspective, the overall picture is what is in the forefront. A dog who is what I call 'bulletproof' around children is a Godsend, but takes a special sort of character on both the part of the dog and the trainer and the family.
Take your daughter out and about often to pet supply stores, hang out at dog parks - - visual and eventually close contact. Get her used to dogs. Ponder all those little details. Think long and hard about the size dog you want. Not one of my kids or grandkids has missed out on snuggling down with fido or running around the backyard, I had two dogs alert me to dirty diapers regularly. A dog will be your family member, you + spouse + child + dog = 'oh my gosh we are a family'. You are in charge, the dog will be low man on the totem pole - but it can be done. Be very very picky and patient - I wish you all the best!