Without knowing the details of your personal situation/exhaustion, take all this with a grain of salt of course. :)
My first thought is that any decision you make now doesn't have to be permanent. If you decide to homeschool and it doesn't work out, then you can send them to school next year (or possibly even mid-year if you're really desperate). And the reverse is also true... if you start public school kindergarten, and you're not happy, you can always pull them out.
There should ideally be a pro/con risk evaluation made for this decision. Since either decision can be reversed, which is the most likely to cause the most amount of harm? Is your personal exhaustion such that your child would be ignored, or even mistreated? Then send them to school. Or would the potential hazards of public kindergarten be the greater risk... many parents report a change in their child's personality, aggression, plus they're more exhausted and likely to misbehave once they're home after school. This doesn't happen with all kids, of course, but it's one of the most common things you'll see mentioned when parents explain why they pulled their kids out in order to homeschool.
If you're just not sure if you would do a 'good job' with a 'solid education' because of exhaustion -- but you're not actually concerned about mistreating your child -- then you should probably give it a try before disparaging yourself too much and counting yourself out before even starting the game! To this end, it's helpful to really understand what kindergarten is, or what it should be. Kindergarten was originally a *preparation* for school, it wasn't 'school' itself. Kids would go to kindergarten to get used to the idea of proper behaviour in a group classroom setting: the social rules like raising your hand, waiting for the bell to go outside, sitting unless told to get up, accepting the teacher as the authority figure etc; as well as getting some exposure (not mastery, necessarily, just exposure) to basic literacy and math ideas.
Much of that doesn't apply to homeschooling anyway (nor does it apply to real life, so if they don't learn classroom social laws until they're older, there's no harm done!)... and basic literacy and mathematical *exposure* is dirt simple. I often like to say, if you don't think you'd be able to pass on early-elementary-school-level skills to your child, then what does that say about your own education, and therefore why would you think your kids would be better off having the same kind of education that would leave them as adults not secure in elementary-level skills?
In fact, you're probably already doing a lot already, just in regular instinctive parenting. Do you read with your child? Sing songs with them? Show them letters and answer when they ask what letters mean and how words are spelled? Do you count toys as you take them out or put them away? Do you make patterns with blocks or baubles? Does she pretend to write letters and notes and maybe even actually write real words once in awhile? Do you do crafts together? Voila, you're doing kindergarten -- and probably in a much more natural, holistic, real-life way than a sit-down classroom way.
It can also be helpful to remember that in some countries, school doesn't officially start until age 7, what we would call grade 2. And those countries have some of the highest literacy rates, and the children are happier because they had a chance to 'finish' their young childhood before starting more rigorous academics. Personally, I've felt for a long time that even if someone doesn't plan to homeschool 'all the way', if it's at all possible, they should at least keep their kids home until they're 7. Not in order to "do school" at home in the meantime. But primarily in order to let them still be kids. There's a HUGE difference in 'readiness' between age 5 and age 7!
If you'd be more comfortable following some kind of guidelines, just for the reassurance, then I'd suggest looking at something like Waldorf style homeschooling. It's designed to not start "grade 1" until age 7, but there are lots of wonderful things to do for "kindergarten" in a Waldorf home. Rather than traditional academics, Waldorf fits more holistically and I'd even say gently into a daily home routine... you find your own rhythm that works for your family. It's based on handcrafts, practical skills, learning about nature, lots and lots of stories and songs and little rituals that kids love, and creative play. There are sources like A Little Garden Flower and Earthschooling and Christopherus and even Oak Meadow (which is more traditionally academic, but with lots of Waldorf influence) that can help you find your path and structure, if that's what you need. You might even find that the focus on 'rhythm' to the day, and peace, creativity, etc etc, might help you find your own peace and rejuvenation!
Anyway, that's just one suggestion to look into. There are of course lots of options that might help you feel more confident. You can always just do NOTHING. Unschool. Just not send your daughter to school and keep doing everything exactly the way you have been up until now. She's probably pretty smart and mostly happy already, right? So why fix it if it ain't broke. Many families unschool for years, if not for the entire length of childhood, and it's amazing what kids will learn when left on their own. This way you wouldn't have to worry about the potential damages from public school OR about your own possible insecurities about homeschooling... you'd just keep the status quo. There's nothing inherently magical about age 5 where they should suddenly start "learning for real". They've been learning all along, and academics are easily picked up when they're older. In fact, they're generally MORE easily picked up when they're older simply because of brain development, so kids who have "learned nothing" for a year or so and then start public school WILL catch up VERY quickly.
Or if you decide that whatever it is that's giving you doubts is too much of an obstacle right now, and that you absolutely need your daughter out of the house for a part of the day (rather than merely keeping her home and not 'doing school'), then you can do that. The risk of damages from a year of school is real -- but slight. At least, of PERMANENT damage. The worst case scenario is that she does a year of K, ends up with problems because of it, and then next year you decide to homeschool and have to spend some time deschooling and reconnecting first, in order to 'fix' the problems. But they absolutely CAN be fixed. So -- if you CAN keep her home, and would prefer to, but just aren't sure, then do keep her home and avoid those possible problems to begin with. But if you CANNOT keep her home, rest assured that many, many parents who did not originally plan to homeschool have successfully pulled their kids and 'fixed' those problems, so you will be able to too, if you have to. (Of course she might be perfectly happy in school too, I'm just spelling out the worst case scenario for some perspective).
Anyway, like I said, without knowing the specifics of your situation this might all just be dust in the wind rather than actual helpful advice... but hopefully at least part of it is helpful??? :)