I don't know much about taekwondo. But it looks like the weight is mostly on the back foot. That is different from most aikido.
I like karate and I know several people who have got to very good levels in both aikido and karate. A few of the techniques even have similarities. A while ago I wrote a blog post called ashiwaza and aikido in the same sentence
. It was mainly about ashiwaza from judo but there are some karate techniques in there at the bottom of the page too. And you have the coherence of a similar cultural background and the Japanese language in both aikido and karate.
One word of warning. In Japanese there is a saying, if you chase two rabbits you end up not catching any. You have to learn new habits and if you start something else too early your body might just be confused. So I personally think after shodan is a good time. It might be worth talking about it with your aikido teacher. There might be ways to do more aikido training instead.
But in the end it is your training and only you can decide what's best for you. Visit both places and see which dojo and which instructor you like better.