Well, for what it’s worth, my first (and strong) impression agrees with others. What you wrote is a reasonable piece of communication, but not at all via texting. What you wrote should have been an email.
Think about the situation from her side of things. To her, you have done something out-of-etiquette, and that’s what I think you are looking to learn in this thread. Remember, there’s no logic to etiquette, and putting your sensibilities from other settings onto this one might go awry.
From your daughter’s perspective, your text is strange. Saying “Too busy now; will respond later,” sounds to her (if not you) rather dismissive and rude. Why? Because that’s automatically assumed on texts anyway. Actively saying you aren’t going to respond is more rude because it’s not expected.
Texts are quasi-one-way communications. You send them into the wind, and you forget about them. The reply might come fast or slow. The reply might come via text or via a different channel. They are the equivalent of chess-by-post. Among friends and family, they represent a single, long, lifelong conversation that needn’t be rushed because, well, we’ve got our whole lives to continue this conversation, and we will.
They are often short yet they should not be trite. An honest reply to your text would be a multi-paragraph email or a phone call, and that needs to be composed, not merely texted. You might have wanted her to say something back like, “Car’s great! Plans are progressing!”, but to her (if not you) that would be a rude and dismissive reply rather than the reply that you actually want to receive and that she actually wants to give. So, she doesn’t even think to reply since the honest, heartfelt response is not suitable for texting. But it’s the original text that set what sort of reply she should give. And she is not out of line by not replying back by text.
If you want more nuanced staying-in-touch conversation, send her emails more than texts.