Indeed. They will take care of you, don't worry.
In fact, this schedule change is actually a great opportunity to get a better flight than you originally had, at no cost to you - yes, you can now negotiate for, and often get, a better flight which would have cost you a lot more if you had booked that originally. I know it sounds crazy, but I have done this many times and it works like magic. Here's what you do...
First, do your homework. You need to be prepared before you call. Using the AA.com website, look up flights that would work better for you. Ignore prices, ignore availability of frequent flyer award seats, none of that matters now.
Now, it's not quite "anything goes" - they're not going to bump you up to Business class or First because of this (unless you're a lot better at working the system than I am...). But because your original flight (that you paid for with AA miles) is no longer an option, they have to get you to your destination on some other flight or combination of flights. And - here's the key to the magic - the substitute flight(s) they move you to must be acceptable to you - within certain parameters (and within reason). That means that you can ask for something better, and if it's available, they will usually do it.
Your replacement flights must start and end in the same cities as your original booking - that is, you must start in in London and end up in St. Louis. And it should depart on the same date (arrival date might be different). But the routing (and the number/length of layovers) does not need to be the same - you do NOT need to go through Dublin and/or Dallas. If you can find an itinerary that's more direct (a one-stop or even a nonstop), and/or one with "better" layovers (better in your opinion) and they have a seat available, ask them to put you on that, and they usually will do it. You are not limited to available award seats - as long as the planes are American Airlines (they have fewer options for putting you on partner flights, but you can still ask). Because it's basically their problem, they are expected to "fix it" for you, and in a way that's acceptable to you.
You need to do the research online before you call, and have all the flight details for what you want ready to feed to the agent (or you can ask them for other options if you want, but in my experience, it helps to spoonfeed them).
I've used this technique many times to get much better flights than I could have booked originally (I switched from a two-stop return from Europe to a nonstop on a nicer aircraft with more comfortable seats and a better flight schedule).
Be prepared with the details of what you have found online that appears available. Be polite, be nice, remember you are asking them to do you a favor. But with a schedule change, agents are empowered to change things more than you might think, and you might as well ask them to change things for the better.
Good luck and I hope this helps!