Are arrival and departure days not an option? Adding an extra day to tickets is usually not that expensive, so on our trips we hit MK on arrival for a few hours. No real plan , just soak it in and see what we can. We then do a full day at MK and do MK on departure day as well. That gives us one full and two half days at MK during a 6night 7 day trip, leaving 4 full days for other things. Some thoughts on other items that were raised:
Park Hoppers - sounds like you may only use them to hit AK and HS in the same day. They aren't right for everyone. I would recommend thinking about it a little more. Being a newbie, there is so much to take in and enjoy. You don't really want to short change yourself at AK or HS and skip things because you feel pressured to get to the other park. It's nice to stop and smell the roses, especially on a first trip.
HS - My DD loved it at 2 & 3. Little Mermaid show, B&B show, Disney Jnr, HISTK play area, etc. Not a full day park though, as others have said.
AK - Also not a full day park but we have stayed there much longer than we expected. Combination of seeing new things we didn't anticipate and navigating a little more slowly than expected.
Universal - sounds to me like you may be trying to do too much, but you know your family best and it seems like the right fit for DS.
Epcot - DD has always loved it and at 6yo there is plenty of must-do activities there.
Park Crowds - Like PPs said, try to plan your days around park crowd estimates.
Have fun on your first trip!