odysseus - I got a dog when dds were 8 and 6. and I really think, that for us, it was the right decision. I enjoyed my mat leaves and working p-t when dds were pre-school. for me, an important part of that was meeting other mums, going to toddler group, Joe Jingles, swimming etc. having a puppy would have made all that much harder work. my choices would have been very much constrained and I would have spent much more time at home and at the park. which might be ok for lots of people - but I do think I'd have had less adult company if I had had a dog and I would have felt that quite keenly.
also, thinking about the dog - when we got him I had started working from home and dds were at school - and I loved my time at home with him. I was really able to focus on him, did training with him everyday, took him into the garden every 30 mins to house train him (he was trained almost instantly) - made lots of effort to socialise him. I was really able to do it all by the book. Of course it's hard to know what it would have all been like if I had had less time for him - but I can honestly say that I found having a puppy pure pleasure and no stress and that we now have a beautifully trained 2 year old. Every now and then you get threads on here from people at their wits' end with new pups - many have bitten off more than they could chew - many have pre-school kids. I'll admit, that maybe we just got lucky and we would have had an easy pup/well-behaved adult anyway.
It's not impossible to do, as long as you truly know what you're in for. but, imho, you'll get more pleasure from both your kid(s) and your dog if you really turn your attention to each in turn.
another aspect - is that dds were involved in chosing and naming our dog. feeding him is their job and walking once a week (we're working on building that up!) and they adore him. my neice - who can;t remember life without hers - really rather takes him for granted. she's just not that fussed about him. that may well just be her - I accept you can't generalise.
good luck, whatever you decide