Hi Bluey,
Your quickest way would be to travel across to Kilcoy and from there, you can choose whether you want to head up to Kingaroy and down the Bunya Highway to Dalby and thence via the Warrego Highway out through Chinchilla, Miles and Roma; or you could head down from Kilcoy to Esk and across to Gatton and up the Toowoomba Range through Toowoomba and then on to Dalby, and the other towns.
There are other ways, but they mostly involve some (often considerable) out of the way travel.
When you take off from Beerwah, head west through Peachester and across to Kilcoy. When you get to Kilcoy, turn just west of Kilcoy if you decide to head through Esk and go through Toogoolawah to Esk. Just as you leave Esk heading south towards Ipswich, the turnoff to Gatton is on the right, still in the speed zone and just across the bridge. If you have GPS you should be able to pick it up on that.
Cheers and safe travels
Dave

I would not recommend the route from Yarraman through Cooyar across to Kaimkillenbun unless your fillings in your teeth have very firm glue in them. I towed my smaller (21 ft) van across that road a couple of months ago and it is very rough for a van. Being black soil, it is quite up and down with not a lot of maintenance on it. It is, however, quite a scenic route coming down through there and swinging off through Wutul to Kaimkillenbun, or The Bun, as it is locally known, and thence to Dalby. The road to Dalby (Irvingdale Road) is an excellent road.