Hi Kimberly & welcome!
Kriston, I love your advice (airplane mask esp).
Kimberly, my kids are about the same spacing as yours and it has definitely seemed too much at times. I was not a stay at home mom until the first three were about 5, 3, and 1. Like you, my 3rd DS presented the most challenges (hence the 3 yr gap between him and #4).
I would have to agree with Kriston that child care was critical. Half-day preschool starting at age 3 became the child care, which helped make friends, socialization, etc., even though most of their early learning was at home (afterschool, which could have nicely segued to homeschool, but didn't for us). We spent a lot of time picking out & reading library books, some math workbooks, museums, parks. I confess I used videos to give myself "free" time--because it's necessary. At your kids' ages, I invested in some educational computer programs and the little kids would have some computer time.
I have found raising HG children to be very demanding and exhausting (but the best thing in the world). Once you have some child care, either in the form of a babysitter or preschool, you'll have more time to explore the testing and school options (including homeschool).