I don't recommend taking that flight, personally. Nothing could make me do a red-eye with a baby & small kids the morning of my cruise departure.
One million percent that. If that flight hasn't been booked, do everything in your power to not book it.
Make sure the infant has a ticket so adults don't have to hold baby all night.
If you rent a hotel room it won't be the daytime room. Those start after normal checkout time. You'll have to rent it from the day before, at the typical nightly rates, so it's sitting there ready for you. Then it's yours until checkout time of 11 or noon depending on the hotel. Because of that checkout time, and housekeeping coming in, and the possibility of wakeup calls etc, sleeping through embarkation is a low possibility.
But landing at 7 means being off the plane around 7:30, luggage around 8 but there will be bathroom stops to refresh, and if staying elsewhere beyond the mco hyatt you'll want to change into Orlando clothes most likely, then getting to the hotel, settling in for just a couple-few hours...
I'm not saying that's not worth it. But you're not going to end up well rested.
I have done the overnight from Seattle a few times and even as a solo traveler it's utterly miserable. Even with a 12 year old who you would think has a grip on traveling since he's been doing so since 17 months old...is miserable.
Annnnd. Having sat behind a group that took up four rows with multiple children and an infant...that dynamic is misery for those around them too. Please discuss appropriate sound levels with everyone agreed of time. There will be people with an expectation of sleeping on that flight.
The flight attendant gave me an extra vodka for free when I finally ordered a specialty drink they had on that flight, after watching me try to sleep and keep getting jolted awake by the sheer volume of the patriarch in front of me... Don't be the people who are so awful the FAs are giving free pity drinks to others nearby.