I’m not sure what it is you need reassurance for with this itinerary, shuigo. It’s not particularly toddler or young child friendly (with some exceptions) so I agree that you should certainly do lots of these plans now before your baby becomes a toddler/young child and starts asserting his/her requirements (it might be years before you could go back to Yasukini shrine for instance)
I don’t think your 7mo is going to all that interested in the zoo inhabitants yet, I hope this is something you are doing for yourselves not LittleShuigo. With a baby, it’s all about them having your attention rather than taking them to a baby park or attraction. They’re more likely to enjoy a long picnic somewhere than being at a restaurant (just like you have already arranged on the 4th April at Kyoto Gyoen), and when you do go out to eat, rooms with tatami are particularly appreciated by the very young.
For the rest of it, it really does boil down to how you expect to move the baby around - carried or on wheels. And then it’s what your baby will allow - personally, I got away with a LOT more carrying a baby, she’d get REALLY bored in a stroller and/or fall asleep and then stay awake through the night (not all babies sleep a lot). Strollers created more problems than solved for us, YMMV. How the baby is fed will also be something that HAS to be factored in - it might be once every four hours, it might be every half hour, even kids who eat at regularly spaced intervals can experience growth spurts that make them temporarily much hungrier than usual. Bottle or nursing will also dictate how you do things, the downside to places with nursing rooms is that you might be expected to use them.
If you’re wanting to go the stroller route, you’ll need to look closely at the paths of the gardens and temples you want to see as so many of them are laid out with gravel.

Can’t help you with Kansai, I haven’t been back there for over ten years either (we tend to go North)