I understand that ship boarding generally begins around noon or 1pm.

However, I was just at CastawayCayClub.com and it said on there that the bus doesn't leave my hotel (Caribbean Beach) until 12:45.

First of all I don't know how accurate this information is ...

Secondly, if it is accurate, considering I'll have 2 young children with me (4yrs and 1 yr), what is the earliest and perhaps best time to get to the port even if it means taking a taxi/limo? There will be 3 adults and the 2 kids so we will have a few pieces of luggage as well (we are doing 8 days in WDW before the cruise including Halloween)...

Thnx in advance!!

I know the terminal has a cafe and TVs for kids to watch movies ... it used to be you needed to get there early to book spa appointments and Palo, but now that you can do that in advance, there is no need to worry about getting there as soon as it opens....
I think your hotel shuttle will probably be fine (they show cartoons on the bus, too).
Maybe someone else can speak to getting the limo....