Young kids like yours will do fine on Celebrity - they do have a very good children's programs for the younger children. And yes, they will get more individualized attention because they will normally be alot less kids than you'll find on the kid-friendly cruises. (It's the tweens and teens on the Solstice-class ships where the amenities are lacking, so you'll be fine with the ages of your children.)
As for when to get the best deal, I always advise the same thing; book as early as possible! It's possible that the rates being offered right now are the lowest you'll find and they may continue to rise. However, if the rates go down, your agent will be able to get the lower rates provided final payment has not yet been made. And you can always cancel up until the final payment due date and get a 100% refund.
Plus, when you book early, you get your choice of cabins and location. If you book late your choices may be much more limited and you may not get exactly what you want.
Also, if you're flying, airfare does nothing but get more expensive the closer you get to sailing. So booking early affords you plenty of time for planning and making the necessary arrangements.
And lastly, booking last minute has the inherent stress and hassle associated with it with tends to distract from the fun of the cruise.
There are a whole bunch of reasons why you should book early and really no good reasons to wait and book later.
But as I said, the Eclipse is a wonderful ship and I know you'll thoroughly love it.