The Gemarah in Sotah says that the reason the Egyptians did not look for Moshe for three months was because Yocheved was expecting for three months before AMROM took her back. From when Amrom divorced his wife and took her back, it was three months.
תלמוד בבלי מסכת סוטה דף יב עמוד א
ותצפנהו שלשה ירחים - דלא מנו מצרים אלא משעה דאהדרה, והיא הות מיעברא ביה תלתא ירחי מעיקרא
How does this fit with (if it has to fit) with the targum Yonoson in במדבר פרק יא?
וישארו שני אנשים במחנה שם האחד אלדד ושם השני מידד ותנח עלהם הרוח והמה בכתבים ולא יצאו האהלה ויתנבאו במחנה.
תרגום המיוחס ליונתן - תורה במדבר פרק יא פסוק כו
(כו) וְאִשְׁתְּיָירוּ תְּרֵין גוּבְרִין בְּמַשְׁרִיתָא שְׁמֵיהּ דְחָד אֶלְדָד וּשְׁמֵיהּ דְתִנְיַין מֵידָד בְּנוֹי דְאֶלְצָפָן בַּר פַּרְנָךְ דִילֵידַת לֵיהּ יוֹכֶבֶד בְּרַת לֵוִי בִּזְמַן דְפַּטְרָהּ עַמְרָם גַבְרָהּ וְאִתְנְסִיבַת לֵיהּ עַד דְלָא יְלֵידַת יַת משֶׁה
That says that in between the divorce of Amrom and Miriam. Miriam married a man in between and had two children אֶלְדָד מֵידָד the time was not three month and should could not have these two if she was expecting Moshe
Menachem
Shalom y'Vrachah,
I found this to be a very fascinating question, and I reviewed over 50 Sefarim to search for the answer to your question. This Targum is discussed at length in many Sefarim, primarily discussing the problem that Yocheved was forbidden to Amram because of "Machzir Gerushaso." In addition, there are many other ramifications that arise from the implied family relation between Moshe, Aharon, and Miriam caused by Eldad and Meidad being siblings (albeit from a different father). There are also other sources that learn that Yocheved married Elitzafan only after Amram had passed away (Seder ha'Doros, Chelek Yemos Olam, ha'Elef ha'Shlishi 2410; see also Pirkei d'Rebbi Eliezer and Rashi in Divrei ha'Yamim).
However, your question, "how were Eldad and Meidad born in such a short period of time?" was not openly addressed by anyone (that I found) but was answered (if I understood correctly) by the Rama mi'Pano in his Sefer "Gilgulei Neshamois"(section "Alef," entry "Eldad u'Meidad" http://www.dafyomi.co.il/sotah/discuss/sotah-012.qa4.pdf) by explaining that the Targum is not addressing their actual physical birth, but rather the spiritual roots of their Neshamos. If my understanding is correct, then the question "how were they born so fast" is not a question, because the Targum is not addressing their actual birth. (I have sent a PDF with the source to the Kollel, and I hope they are able to forward it to you.)
Berachah v'Hatzlachah,
Shimon Brodie