She's extremely young, and many of the kids in her class may be 6-12 months older. That's a big range. She's only been in kindergarten for a few months - so give her time.
The teacher says she has friends, so I'd relax. If the Daisy thing doesn't seem to be a good fit, then try something else. Try really, really hard not to compare her to others in the family! While looking at her "deficiencies" you are missing all her positive attributes and abilities.
I wouldn't waste time trying to decide if she's on the spectrum, especially since none of the professionals see an indication of that - we are quick to reach for a diagnosis when sometimes kids just need to time to develop into who they are and want to be. It's a time to explore and experiment - let her do that.
I'd caution you about yearning for her to be a part of a clique! If you look at a zillion questions & responses on Mamapedia, you'll see that cliques and exclusion are far more of a problem than an asset. You'll also see a lot of questions about parents being heartbroken over something like the "tickling" remark you mention. Who knows what your daughter was talking about? Maybe someone else said something a minute earlier and she thought about it, then came out with her comment. It could be anything. But let it go and move on. We just can't get heartbroken every time our kids say something that's a bit on the clueless side.
You say your daughter has made great strides in a smaller environment, so kindergarten's larger class is a big adjustment for her. It can be so overwhelming for so many kids. I'm sure she's not alone in this regard. She's progressed before, and she'll continue to progress. Look at some small group settings now and then for her - maybe the library story hour or art class would be better for her. Don't over-enroll her though - too much scheduling is a problem (ask the teachers). But a once-a-week program for an hour might be fun.
Meanwhile, encourage your daughter to seek out another quiet kid or notice the child who is sitting alone at lunch or not engaged on the playground - that's the child she should be drawn to for one-on-one interaction.
And to save time, we do use abbreviations like DD for daughter and DS for son, DH for husband, MIL for mother-in-law, and so forth - so you don't need to explain your abbreviation every single time for us.
You mention being an older parent. I'm not sure how old you are, but I was quite a bit older than my kid's friends' parents, and my husband is 4 years older than I am. It's okay! You can still connect with other parents in your child's school (far more are older than you might imagine) and many of us here are giving advice from back when our kids are little. Your friends may have more input than you think even though their kids are older - and you don't want to compare anyway. Sometimes hearing that things worked out just fine for others' kids who were a lot like your daughter can help you feel more confident.