Wa Alaykum Assalaam Warahmatullaahi Wabarakaatuh,
It truly is a wonderful ambition to become a da'ee of Islam, and to be a da'ee, you don't need to be in any particular organisation. Your work is for Allaah (swt) alone. If you limit yourself to simply wanting to become an important member of a particular organisation, then you must question your intention. And the importance of having the correct intention cannot be over-emphasised. Your purpose is to attain the pleasure of Allaah (swt) and that can be done in so many ways, even by teaching your own family and community.
Regarding the career choices, there are a number of things to consider. First of all, it is not necessarily true that just because someone is a doctor, people will listen more carefully to what they have to say about Islam. What is more important is their study and understanding of Islam. So you can have a person who spent decades studying Islam from respected scholars and yet have a simple profession, and someone who is a leading doctor and only studied for five years or so... which one would you trust more with regards to Islamic knowledge? There are many examples of Islamic scholars who had such humble professions yet were widely respected for their deep knowledge and understanding of Islam and their sincerity, piety etc. So do not choose a medical career on this basis alone.
Medical courses are typically long and require a high level of commitment, so you must choose it out of certainty that you want to be a doctor. Try to get some work experience to understand what being a doctor truly involves, because it may not be what you imagine. Remember also that for a sister, you must think about work-life balance... some sisters find a conflict between the difficult work patterns of a doctor and married life, raising children etc. I don't know what this is like in Pakistan, but it's something to look into. There is also the issue of moving away from home and whether there is any mahram and so on...
So think about your long-term goals carefully and consider how your course will help you to achieve them, and as brother Salahudeen mentioned, which one you really feel content with. Above all, make plenty of du'aa, perform Istikharah and place your trust in Allaah (swt). May Allaah (swt) make your intentions pure and guide you to the best decision, Aameen. Forgive me if I said anything incorrect.