This question deals with a real life issue—the naming of a precious child. Judaism takes this matter very seriously. There are many traditions attached to the procedure to be followed with naming a child. Traditions are usually community driven.
As is well known, the naming of a Jewish male child is part and parcel of the b’rit (bris) milah ceremony (circumcision) held on the eighth day after the birth, of course assuming that the child is in good health.
For a female child, the naming is not necessarily tied to a specific day. However, it is usual to do the naming in the context of having the Jewish father (or in the absence of a father another close individual) honored by being called up to the Torah for an aliyah—reciting the berakhot (blessings over the Torah reading) in the synagogue service.
This can be accomplished more modestly or with greater pomp, depending on the desire of the parents and custom of the synagogue. Within much of Sephardic Jewry a ceremony known as Zeved Ha-bat (“the gift of a daughter”) is practiced for the naming of a girl and the text for the ritual is to be found in many traditional Sephardic siddurim (prayer books).
This text is making its way into the Ashkenazic world as well, with its introduction quietly into the Authorised Daily Prayer Book of the United Hebrew Congregations of the Commonwealth, with new translation and commentary by Chief Rabbi Lord Jonathan Sacks. This highly recommended Jewish prayer book appeared in 2006.
Subsequent to the appearance of Rabbi Sacks’ siddur for the British Commonwealth, is the phenomenally successful so-called “Koren-Sacks Siddur” published by Koren Publishers, Jerusalem together with the Orthodox Union (USA). This attractive, much beloved and expanded siddur, first appeared in 2009. It appears in many formats and is also highly recommended.
Returning to your original question of naming a female child after a beloved grandfather, this is a common Jewish practice. The most accepted Ashkenazic practice is to name a child only after those who have already passed on. This is not the case for most Jews who consider themselves to be Sephardic or Oriental Jews, where they frequently honor their closest living family members by naming newborns after them.
We often find that the names given can be the exact same name for children of the same sex or names reminiscent if the child is of a different sex. There seems to be great flexibility in the specific Hebrew name to be bestowed upon the newborn child. We regularly hear at the naming ceremony or at the seudah (festive meal) following, an explanation of the name and why it was chosen. This is the opportunity to share with others your true intent and feelings.
Jewish naming books can be found in synagogue libraries and public libraries; and in larger bookstores in areas with Jewish populations, as well as online.
Just a couple of thoughts for a female child being named after “Meir Eliazor (Eliezer)”: you can consider Miriam Elisheva or Mira Elissa (or Elise). The field is very open, indeed.
Wishing you mazal and good health!