I recently purchased a small cabin. It is quite old but, has new plumbing. For the first a day or two the toilet flushes with no problems. After a couple of days the toilet bowl will fill up to the rim but, not overflow. Sometimes it will empty slowly and othertimes it will stay for days. We have tried plunging it and using Draino. The septic tank is supposed to be new and we only use the cabin for about a week a year. Is there something I can do to fix this or do I need to hire a professional??

Have you had anyone inspect the tank? New or not it should be inspected to insure it is operating correctly. You should skip the plunger at this point and try a toilet auger. That only reaches about 4' and if the clog persists you may need to pull the toilet and rod further from that drain.