Yes, there are multiple flights from Bangkok to Kuantan for under ฿ 11,999. The cheapest flight booked recently is on Malaysia Airlines for just ฿ 10,919, but on average you can expect to pay ฿ 10,919.
There are no direct flights from Bangkok to Kuantan, but Cheapflights can provide you with all the information you need to find the fastest route with the fewest stops.
You can imagine temperatures to be in the 36 °C range in April. The weather in Kuantan is generally colder than Bangkok's. As flight availability is subject to become more limited as peak season approaches it is ideal to book in a timely manner.
For as low as ฿ 10,919, Malaysia Airlines can have you in Kuantan from Bangkok in 7h 05m.
Currently priced at ฿ 10,919, Malaysia Airlines will fly you from Bangkok to Kuantan and back. In addition to Malaysia Airlines, many other airlines offer competitively priced options for your trip.