I think you already answered your own question
. There are different approaches to starting "school" when you are homeschooling. The Charlotte Mason approach would take a fun and gentle introduction of letters, numbers, counting, etc when the child is ready, not before and not after. Teaching about the Bible, exploring the world, taking advantage of a child's natural curiousity and openness to instruction at a young age to get them started on a lifelong love of learning. What I would say a lot of preschools are doing in order to try and prepare children for school and improve test scores, etc, is requiring too much of children too soon. Especially in the area of fine motor skills. Children in school are required to do a lot of writing right now. If they aren't ready at 5 years old to do that much writing, it becomes difficult, they can't do it well, and they then feel that school work is too hard and don't want to do it. The problem is that fine motor skills, while they can be refined by practice, don't develop until they develop and having a child do too much writing before they are ready is counterproductive in so many ways. Or reading. Some children just aren't ready to read until they are 7 or 8 (or maybe even older). That's just how they are made. If they are made to feel like they are dumb or behind because they can't do it yet, that's when early education or early instruction goes wrong.
So I hope that makes sense, if your daughter is able to do the activities and is enjoying them, then she is doing great and so are you! Homeschooling allows you to avoid some of the pitfalls of early instruction because you can see your child's frustration or struggles much more easily than a teacher with a room full of children can, and you can also adapt your lessons and instructions to allow them to flourish. And then of course there's the spiritual component too which I think is more important to those of us who homeschool than even the ability to tailor our teaching to each child's needs.
LHTH seems to be just right for most preschool age children, obviously they have written it with them in mind. It has fun learning activities that tie together and help the child develop skills they will use for future learning, without expecting too much of them in the reading or writing department at too young of an age.
I keep reading that experienced homeschool moms believe that letting kids be kids while they are young is more benificial in the long run, than starting school too early. Makes sence to me, but my daughter fits into the age range for this program and she loves it. It's play to her! Is the key not to get too crazy with with workbooks and formal schooling? I don't want to burn out my 3y/o 
No matter how far I get to run, though, it's my time where I'm not responsible for kids, a dog or a husband