Women are just as obligated in Melaveh Malka as a man. However, you don’t need to wash and eat bread, you may just et fruit etc. it is better if you can eat a Mezonot. During the winter then maybe, you should try to wash and have a small seudah.
Explanation:
The Gemara in Shabbat 119b: R’ Chanina said a person should always set up his table (to eat) on Motzei Shabbat even if he only eats a Kazayit. Hot water on Motzei Shabbat (for drinking or washing) is healthy. Hot bread on Motzei Shabbat is healthy. R’ Abahu would have a fat calf prepared for him on Motzei Shabbat and he would eat the kidney. His son Avimi asked him why waste a whole calf , just leave over the kidney on Erev Shabbat. They did that and a lion came and ate it.
The Shulchan Aruch OH 300: One should always sit his table on Motzei Shabbat to escort the Shabbat out. You only need to eat a Kazayit.
The Magen Avraham writes the Gemara says that eating meat on Motzei Shabbat is a god thing. Look in Siman 291.
The Pri Megadim and the Machatzit Hashekel disagree what the reference is.
The Pri Megadim understood the Magen Avraham was referring to 291:6 where the Shulchan Aruch rules that women are obligate din Seudat Shlishit and the Magen Avraham means that women are only obligated by Seudat Shlishit but not Melaveh Malka. The Pri Megadim argues that they are.
The Machatzit Hashekel understood that just as women re obligated in Seudat Shlishit they are obligated in Melaveh Malka. Just as the Magen Avraham himself explains over there that women are obligated in all Mitzvot of Shabbats like men. Which would certainly include Melaveh Malka. So rules the Kaf Hachaim (300:2)
The are three reasons mentioned why we do Melaveh Malka.
Rashi writes simply that it is Kavod Shabbat to escort it out like someone who escorts someone leaving the city.
Ein Eliyahu writes that Melaveh Malka shows that Shabbat was not a trouble, just like a guest who we were happy stay one more meal.
The Taz quotes the Shiblei Leket there is limb in the body called the Niska and it only gets nourished on Motzei Shabbat. The Mateh Moshe writes that this limb is called the ‘Luz’ and it is from the luz bone which the person will be rebuilt for Tchiyat Hameitim. This bone does not decay in the ground after death. Nor can it turn to ash or get ground up i.e. it is indestructible and from that bone a person body will be remade and it is that bone which gets pleasure or feels pain after death. The Elyah Rabbah adds that since this bone only gets nourished on Motzei Shabbat so when Adam Harishon ate from the Etz Hadaat it didn’t get any nourishment and therefore the curse of you will return to dust does not apply to it.
It would seem that these three reasons apply to men and women equally. The Torat Shabbat however sys it is a timebound mitzvah not directly connected to Shabbat, and women are exempt.
What should we eat by the Seudah?
The Gemara seems to say that one should have a hot drink hot bread dn meat. The Magen Avraham writes that nowadays when Seudat Shlishit is so late and you are too full to eat one may just eat fruit. The Mishna Berura writes that Melaveh Malka is not an obligation like Seudat Shlishit which is sourced in a passuk, but it is just a mitzvah therefore Seudat Shlishit has priority if he cannot do both. The Shaar Hatziyun adds if he has only a little of meat and fish it’s better to eat them by Seudat Shlishit. The Pri Megadim writes that unfortunately over time many people became less particular about Melaveh Malka but is good for someone to make small seudah on Motzei Shabbat.
R’ Ovadia Yosef writes that that is a mitzvah to have a fourth Seudah on Motzei Shabbat and if he can’t eat bread then he may eat fruit. Women are also obligated.
There is great importance eating Melaveh Malka but the three seudot on Shabbat are more important so one should focus on those. One should try to eat Melaveh Malka even if it is just fruit.
The Maaseh Rav from the Gra said someone wanted to go to sleep after Havdalah and he told him even fasting a lot will not make up for one missed Melaveh Malka.