This is a great irony that all of the travellers do face. As per Dubai rules, your visa must be at least 6 months from first issue and should have atleast 3 months validity before expiry. so when you are new in qatar, your window to travel is only 3 months in the first year.

however the above is theory - normally you can travel if you have been in other middle east countries and also your profession. I have travelled after one month of my visa stamping.

However the options are to take an advance visa before travel - any hotel in dubai that you are staying with can arrange the same or even emirates airlines. A bit of insurance is always better

regards