Tips - moving to Dubai in few month

1.  Usually the employer puts up the newbie in a hotel at least for 2-4 weeks, if not longer.  Ask for this.  In any case you would need to be in a hotel for a few days before you get an idea of where you need to stay, and find a sharing accommodation or rent an apartment.  Most decent companies would assist an employee in this regard, including advances for rent etc.
If this does not happen, prepare for at least AED 3K per month expense towards accommodation on a temporary basis.
2. If you have a friend or relative, he may be able to assist you with a temporary accommodation on arrival.  Otherwise book a hotel for a few days, which can be done in advance, then follow as suggested in (1) above.
3. The Visit Visa (or Employment visit visa) arranged by your employer would be valid usually for 60 days to enter Dubai, thereafter valid for 30 days from date of arrival.  You have to plan according to this.  With your present employer you have to work out an amicable solution.
4. Much depends on house rent, school fee (if you require for a child) and your lifestyle. Difficult to say without more info.   As a sketchy guide you can expect to save 20-30%.
5. Thousands of women work here.  They find jobs just like anybody else and anywhere else.  As easy or as difficult as anywhere.
6. Dubai is very safe for women, working or otherwise.  One of the safest countries in the world, at least for the present.