If you feel that your dragon is not doing well due to the presence of the male then I think it is obvious you should separate them. That is the most conservative course of action. If you wish to breed them or house them together at a later time when both animals are thriving then you can try again.
Dragons can be kept successfully alone, in pairs, trios or groups. This is nothing new and many long time breeders have done this for years.
I do think keeping them together is more complicated. Some animals seem to thrive no matter what you do and others are very sensitive and never seem to be as robust. They have different personalities and do well or not in different situations. In this way I think it is very important to take each instance on a case by case basis. Generalizations (like this is always right and always works or this is wrong and never should be done) are often times of little use. Of course your understanding and the husbandry you employ are primary.
If you are new to beardies or reptiles in general, it may be best to develop a good understanding of them by housing them alone first. Get your animals thriving, learn about them and what they do well with and what they don't. Then you can experiment after you have a solid base to work from. Then you can make better decisions when things get more complicated. Of course they are your animals and you may do what you like with them. Just understand that you are responsible for their well being and they are the ones subject to the consequences of your decisions or lack thereof.
Good luck,
Ian