With my dd I was obsessed with the fact that something would go wrong with the dog... Or otherwise that baby would be allergic and she'd have to go! Looking back I realised that I had crazy hormones and was worrying for no reason. My dog has always been fab with dd and actually she behaves better on the lead when I have the buggy than when I don't. We did practice with the buggy beforehand as I wanted to work out what worked best. A few new commands were needed - beep beep which meant get out of the way, then behind which meant walk in line behind me and the buggy. Plus perfecting her sit and stay was essential for getting the buggy out the car etc, so I made sure I always had treats in the early days.
Other tips we were given were before baby, try to teach the unexpected. We were actually given this advice when we first got her as a puppy as friends knew we wanted kids but it was invaluable advice for when baby turned toddler! Examples were, don't expect walks at set times, don't take food unless given permission (e.g thrown from highchair/out of hands) but then more random things like when she was half way through her tea, picking it up and putting it on the side for 5 mins then giving it back. Teaching give as a clear, firm demand so any toy will be released from a distance etc! Luckily this paid off as not one of dd's toys was had and when little hands try to help her eat or she gets help to wag her tail we haven't even had a flinch. The dog still has her crate where she sleeps and we kept this as a safe space for her where dd must not go so she always has a chance to retreat if necessary! Whilst you try to never leave them alone there will always be times you don't realise!