I would bring my own. If you are flying, you will have it in the airport (definite plus). You can simply gate check it.
Also, I would not do mini golf with a baby. I would do more parks! Three days and only two parks? No DAK? That park is so lush with foliage, and there are so many animals to see.
We don't go morning to night, but also do visit a park daily when there. Often it's just a few hours at most.
Disney Springs is a huge outdoor mall; not interesting to a baby (or me).
I would definitely want my own, though. Don't see the point in renting a similar one to what you own, if you have it.