We have DD (11mo) and a cat. Reasonable garden. I will be working 2 days a week shortly. I would love to have a dog and am thinking it's not a bad time. We've just had guests visiting with one and it was no trouble (despite being enormous). DD loved it, cat didn't. She (cat) didn't go in the rooms it was in, but avoids the baby in the same way. DD didn't like dog barking, but otherwise followed it around, laughed when she saw it, looked for it if it went out of sight.
I'm thinking small - medium rescue dog but having just browsed the local dogs' home sites, it appears they don't tend to rehome dogs with young children. Am I being unrealistic? I don't really want a puppy, due to being out two days a week.