My dad, with the best intentions possible, bought me an 8 month old filly when I was a young teenager so we could "grow up together" - he and his friends had horses back in the day and I had taken some riding lessons so we felt qualified for this. She bit my arm when we went to look at her but I stayed quiet because I didn't want to lose this opportunity. She kicked me when I tried to groom her, she kicked my dad and his friend when they tried to "train" her, and for the next year or so she became a nightmare to be around (100% our fault as inexperienced horse people, not hers). We ended up giving her to our neighbor who ended up neglecting her, and since moving from my childhood home I never knew what happened to her.
My young life would have been completely changed if, instead of a young horse that needs training, structure, and skill, my dad bought me an old horse that just needs to be loved on. I now have two yearling colts (one just recently gelded, the second soon to be) and I'm older and wiser, most importantly qualified to train them, and I love them to bits, but still I wish I stuck to my original plan to get a couple older horses that we could love on. It is stressful making sure I won't fail my yearlings, every single moment is a training moment with young horses and if I miss some of these moments they can go south very quickly.
You will hear many reasons why it will not be a good idea to start with a young horse, or an ungelded horse, and as always there are exceptions to the rule, but I cannot stress enough how much more fun and rewarding it will be for you and your daughter to start with older, experienced horses. Seriously, even if you only have a few years with an old horse it will be the most enjoyable few years you can have, then that experience will allow to you expand into challenging adventures with horses if you want.
Another relatable story, we have a single mom neighbor down the road that purchased a baby jack donkey for her daughter - some months later they realized the donkey needed a friend so they got a pony colt to be his friend. They have no horse experience and the animals live in a very small, asphalt area - they are now 2 years old and the biggest pushy, bitey monsters you can expect two mis-trained, cooped up, young male equines to be. The daughter is scared of these animals (that were purchased for her to love) and for a quick moment we thought about taking them in before we found our current boys. We are extremely glad we didn't go down that path - after that behavior has been learned it can be so difficult to undo.
