The short answer is yes, it's definitely plausible to do this. You have plenty of time to build up your mileage, to get to where the marathon doesn't wreck you for weeks or months afterwards.
The long answer is it's going to heavily depend on what you do for that marathon training.
I'm a personal trainer. In my experience with clients or gym members and half marathons and marathons, practically all of them make the same mistake.
"I'm going to train for a marathon. It's in six months."
Five months later. Me: "How's the marathon training going?"
"Started slow. I didn't start running until two months ago, but it's going pretty well now. I've gotten to where I can do 10 miles at a time."
I routinely see people be able to run around half the distance, then on race day, think there will be nothing wrong with trying to double their mileage in a single day. Even trying to make up the difference with a lot of walking is likely to hurt.
The fact you're even thinking about things this far out is a great sign -time is your best friend when training for a marathon- but I have seen this mistake too many times to count. Even Lance Armstrong did it. After the NYC marathon,
“I can tell you, 20 years of pro sports, endurance sports, from
triathlons to cycling, all of the Tours — even the worst days on the
Tours — nothing was as hard as that, and nothing left me feeling the
way I feel now, in terms of just sheer fatigue and soreness”
This matters because your training before the marathon will heavily dictate how you feel after the marathon. If you don't do enough beforehand, that marathon can range from feeling really hard, to the hardest thing you've ever done, to stress fracturing your foot and not being able to run for months afterwards.
My limited experience with people who do their due diligence in preparation for a marathon -think having already run over 20 miles in training (only having done 20 is still kind of low)- is they take it easy the week afterwards, then they start lightly running again. By 10-14 days, certainly by a month out, they're fine, to where a half should be plenty doable.
The less marathon like your training is the more unpredictable how you'll feel will be, which means you might not know if you can do the half until after you've done the marathon. But if in training you know 23 miles has felt solid, and running 10 miles a week later also felt solid, then 26 will probably feel solid too, as will running 12 miles a month later.