Hi Helen!
Welcome to homeschooling and HOD!!!

I think it does sound like a good idea to get both the K and 1st options for your DD if that is what you think would work best for her and your family! My DS, who is now 6, was 5.5 when we started K last fall and was in preschool for the two years before that. He was in a special advanced group at preschool and had learned most of his letter sounds, etc. by the end of his 4K year. I share that because I have still taken LHFHG slowly with him this year and it has been a WONDERFUL year for him!

I am sad to say that I pushed my oldest DS way too hard his K year and have regretted that, so I decided that my second DS's K year would be much more gentle and mostly FUN, which is what K should be, IMO!!!

Despite doing things slowly, he is reading REALLY well right now (we have used The Reading Lesson-LOVE it!) and is probably at the end of a 1st grade reading level -- I couldn't be more pleased!!!

Earlybird Math has been mostly easy for him, but I felt like it would be good for him to still go through to reinforce basic math concepts since Singapore starts moving pretty fast once you get to 1B.
Something to think about also is that you may find that you need to slow your DD down when you get to Beyond for 1st or Bigger for 2nd. There is a huge jump b/t Beyond and Bigger as far as writing, narration, etc. We did LHFHG half-speed until January and I only sped it up to full-speed b/c my DS was begging for more!

We are ending his K year with about half of it finished and are going to do the rest of LHFHG with the 1st grade options next year for 1st, which will cause him to do Beyond for 2nd and Bigger for 3rd (this is what I want, having taught Bigger for 2nd with my first DS)!

All that to say, there are so many ways to make HOD work for your family and I know you will find what is best for yours!!! HTH a little!!!