Wa Alaikum Assalam Dear Sister,
Thank you for your question and for contacting Ask About Islam.
Idealistically, the choice for working or not working should be up to you and only you, as long as you abide by Islamic principles when outside the house. However, the culture in some societies defies Islam, since in Islam, the women has a major role in society whether at home or at work.
There are extremely smart Muslim women scientists, who can serve Islam better than many men. The question remains: Why educate women if they are going to stay home? If her place is at home then she should only receive Islamic knowledge in order to pass it on to future generations.
Some might say that this is not a bad idea! But how about female physicians; should they also stay home and let other women who prefer female doctors to see male doctors. Do we make an exception for those women only; this is not how Islamic law works.
In Islam, if a woman is allowed to go out in society to shop and do other things then she should also be allowed to work.
According to Islamic traditions at the time of the Prophet (peace be upon him) and after his time, women fought in wars and did whatever they did best in society; they were not isolated as many men wish them to be in our modern time and age.
Also Aisha (may Allah be pleased with her) used to teach fiqh and hadith to seekers of Islamic knowledge whether males or females, until she passed away.
So there is women ambition in Islam since Aisha was not doing so for money; her ambition was purely to serve Islam, yours is to gain additional knowledge and experience in your field to hopefully serve Muslims better in the future. There is absolutely nothing wrong with that.
On the other hand, if a woman is working, she should not neglect her husband and children by giving priority to her job. She should be able to balance between the two; if she can’t, then her family has priority over her work.
I hope this helps answer your question.
Salam and please keep in touch.