It's not a matter of meeting my asking criteria and I am not trying to be rude, you really left a lot out of your inquire and there is not a simple answer to your question.
Even if I were to assume what you meant I still don't know the type or thickness of the material you want to burn, if you have a feed rate in mind or anything, so again it's not a simple answer.
Your power supply puts out about 6v but how much current?
If you can give more information there are people here who can point you in the right direction.
As most laser diodes will need a current regulating driver you may find it more convenient to use rechargeable batteries if your device is to be portable.
If you want to build a cnc type x/y axis burner cutter then you could incorporate your power supply but it will have to power a current limiting driver, or you will have to build a limiting circuit.
What ever your burning purpose be aware that any laser over 5mw requires eye protection, laser safety glasses that attenuate the wavelength that you are burning with.
There are burning lasers in hand held wands that will run on 3 to 24 volts with their own buck/boost limiting driver built in that are not expensive, but you must buy the safety glasses first.
Much can be found on ebay
But remember to buy laser safety glasses to protect your eyes before ever trying to burn with a laser, sun glasses will not work.