Bringing a rental car would be a huge hassle & expense.... if u they even allow it. This is not the US. Owners of pvt cars often have to reserve vehicle space weeks, even months in advance -- huge space in the big ferries goes for 18-wheelers with supplies FOR islands and goods FROM islands (Naxos sends truckloads of Marble to Athens every week).
If renting in Naxos, visiting Santorini, returning to Naxos, do NOT keep the car; just re-rent upon return. If you sta y somewhere sensible like Firostephani, you won't need a car -- bus up to Oia & Back, And from Firostephani walk in 15 mins to Fira, on a level flagstone walkway parallel to the main road. (ask your hotelier). Use a cheap "cane stroller" for this, and frankly you should bring one for use on entire trip, then toss it or leave it with your last hotel. I have had two 2-year-olds; they start out liking to walk and then suddenly collapse, and are way too heavy to carry.
If you are only staying 24- 30 hours in Santorini, you will not have much time to "explore"... and unlike Naxos, which is the largest Cyclades Island, with mountains, hillside villages, amazing inlands -- Santorini is just 12 miles long, and in 24-30, you can see OIA, FIRA town (& its good museum), enjoy the caldera view, MAYBE go by taxi to Ancient Thira and that's about it... especially with a 2 yr old who may melt down & need a nap.
Your Ferry options are (1) 10:40-arr 11:55 ChampionJet -- large car-carrying catamaran... has small back deck for brief viewing as u enter caldera -- it's fast/short trip but about 2x as much €€ as (2) BLUE STAR 12:50 arr 14:50 large open-deck vessel.
Return options: Same large Champion Jets @ 10:45 & 12:25 and BLUE STAR at 3:30. So your max time would be arrive noon, and sail next aft @3:30 (but u must be at dock before 3). If u tak my advice & stay in Firostephani, a scenario might be:
DAY 1 -- ARRIVE NOON -- check into hotel. Walk rim path, enjoy view. Your window of opportunity to see OIA is about 3 or 4 pm ... the cruise crowd leaves about 3, and the village & views will be relatively uncrowded for a few hours (you can take the local bus from the Firostephani stop on main road; a taxi will cost you about €20-25). By 6 pm, LEAVE! (the mobs re-invade for the supposed superior Oia Sunset) ... you can find a restaurant in FIrostephani or Fira town that will enable u to enjoy the view, and also welcome a toddler. In Firostephani, look at Aktaion taverna... in Fira, check rooftop terrace at STANI taverna.
DAY 2 -- 9 AM - Explore Fira Town & Museum (small, good, u can cover in 30 minutes). I do NOT think you want to attempt the Akrotiri excavation with Junior. You could take cable car down to the old pier & back. Then whoops! time for the ferry!
