Connection time between the airports is app 1hour

  Regulations for carry-on baggage

Getting to and from the airport
Vibhavadi Rangsit Road is the main route linking DMK with downtown Bangkok. Other transport webs bringing us to downtown are toll-way and expressways which facilitate passengers' trip with more convenience and fastness.
Besides travelling by road, train is other choice for travelling to town, spending 30 minutes only. The railway station is opposite and linked with the airport by walkway bridge.

There are several kinds of transportation services provided for passengers such as limousine of Airport Associate Co., Ltd. and of Thai Airways International Public Co., Ltd. car rental service, taximeter and airport bus.

Information Counter
Airport Information Counters are in the passenger hall and passenger lounge of domestic passenger terminal. Airport information officers are willing to give necessary information to passengers with Thai courtesy.

Terminals

Domestic Passenger Terminal 1 

Above information by Airports of Thailand PCL

Hints:
You will receive many offers for taxis and hotels just before leaving the arrival zone!  Ignore them. Say: "no thank you".  Most of these services are too expensive. After leaving the arrival zone without losing money, you may wish to first visit one of the currency exchange services.   That's ok!  Do it.
To go to Bangkok now, you will need a taxi. There are private taxis called taxi and public taxis called taxi-meter. Take a taxi-meter, because it is much more cheap. Some private taxis pay money to the airport, so they have a better location for waiting for passengers.
Money-Hint: Use the exit on the third floor (departure) and ask an incoming metered taxi for take you to your desired destination. These metered taxis generally come from Bangkok to carry passengers to the airport.  Here is the best (and cheapest) place to get transportation to Bangkok central.
How to "use" a taxi: First, tell the driver your destination.  If the driver likes that, tell him you want transportation "by meter".  If he still agrees, you have your first golden deal.  We highly recommend to enter the taxi now!  Let him use the "express road" and give him the tollway fee (40 Baht).  Finally, you will pay estimated 250 Baht (depending on destination).
If the traffic is very busy in Bangkok (it happens sometimes...), many drivers do not like to go "by meter" and you must bargain for the price. You should not accept more than 70% of his first offer.  Do not enter the taxi before fixing the price!   Finally, you will pay 300-500 Baht (depending on traffic and location).
Hotel: You can book a hotel at one of the counters in the airport, but take note of the location and the price, but this is not the best idea!   Try to book a Bangkok hotel before arriving ... over the Internet.