I'm not the parent of a type 1, but was diagnosed at age 4 and can answer some of your general questions.
Pumps are ideal for infants and kids because they deliver such small doses (.025 of a unit). The base rate of insulin varies throughout the day, so pumps let you tailor it to individual needs. Then you take more based on # of carbohydrates eaten and current blood sugar. Most people use fast acting insulins like Novolog or Humalog, but because young kids are super insulin resistant they sometimes use the slower insulins like Regular. No need for the long acting stuff like Lantus or NPH.
Some parents of infants get diabetic service dogs to alert parents when a young child has a low blood sugar. Google "diabetic service dogs" and you'll find information. Most people just have to check their kids in the night. I was diabetic a few years before glucose meters were sold, but my mom could tell I was low in the night because of the usual symptoms (sweating, shaky). Your doctor should set a higher target blood sugar for a child to offer a little buffer so you can avoid most lows. If needed, it's okay to decrease pump's basal rate a bit to avoid an overnight low.
It's a lie that your child won't know the difference because he/she is diagnosed early. A person is a person. You still feel pain when you get a shot or crave sweets or want cake at a birthday party like anyone else. Thanks to carb counting and glucose meters it's much easier to be a diabetic these days. Still, your child will have some point where he or she will probably rebel against being diabetic. It's normal, especially in the teen years.
The children with diabetes website has a lot of great book recommendations. Anything marked highly recommended is a good pick. www.childrenwithdiabetes.com/d_06_b00.htm
I've had diabetes for 34 years now and have no complications. I have a young son whose not diabetic and a great marriage, busy job, and good life overall. I'm nothing special and have never been a slave to caring for my diabetes. There are a lot of us out there. Know that there is no reason your kids won't have good lives. You'll just do things a little differently and probably become REALLY good at math after all the carb counting!
Take care and be sure to share your experiences. There don't seem to be a lot of infants with type 1, so what you have learned will be a big help to others.