Booking with Peach Airlines

Is it necessary to book a flight much in advance in order to secure the best price or are their prices fixed/stable?

I want to fly from Kansai airport to Fukuoka the day after i arrive in the airport.

I would like to delay buying my ticket as long as possible. How long should i wait?

My flight to Japan is 10 March.

I get their promotional email - they tend to have a lot of sales - I think I saw one for the beginning of March already. So if you book early you might save some yen.....

I have already bought my ticket for a trip from KIX to Seoul in April.....

Airline prices vary a lot over time, in both directions, and domestic flights in Japan are no exception. The fare you are seeing now could be gone tomorrow (or even in an hour).

This one is no different to Jetstar. So book them ASAP when you see sale.