Two other members of her family were wounded when a tank round hit their home east of the town of Khan Yunis, a doctor said.
At least three other Palestinians, including a civilian, were also killed in Israeli attacks on Wednesday.
Mark Regev, an Israeli spokesman, said that the government was in "support of Egyptian efforts" to mediate a ceasefire agreement with Hamas, which has ruled Gaza since it seized full control of the territory last June.
"The security cabinet decided this morning to support Egyptian efforts to achieve calm in the south and to end the daily targeting of Israeli civilians by the terrorists in Gaza," Regev said.
"In parallel, the security cabinet has instructed the military to continue its preparations in the unfortunate event that the Egyptian track should prove unsuccessful."
Hamas was dismissive of the Israeli announcement.
"The Israeli occupation itself says it is preparing a large operation in Gaza, which demonstrates that its declarations on a truce are neither realistic nor serious," Sami Abu Zuhri, a Hamas spokesman, was quoted by the AFP news agency as saying.
David Chater, Al Jazeera's correspondent in Jerusalem, said that Israel is "preparing for a heavy military incursion into the Gaza Strip".
"Many ministers are saying ... that it's important that Israel should launch a heavy punch against Hamas before any truce is concluded," he said.
"The security cabinet met for about four hours ... the decision is, apparently, that the Israeli's will continue to explore the options created by the Cairo initiative for the six month Gaza truce.
"So one hand is being held out towards peace, towards the idea of a truce, while the other one is a bunched up fist ready to hit Hamas and the Gaza Strip hard."
Israel pulled out of Gaza in 2005 but still maintains a harsh blockade on the territory. It has in the past restricted fuel deliveries to Gaza, resulting in widespread and protracted power cuts.
The Israeli government has made it clear that its agreement to a truce remains conditional on making progress towards the release of Corporal Gilad Shalit, an Israeli soldier held by Hamas for the past two years.
But even as meetings in Egypt got under way, the violence in Gaza continued.
An Israeli military spokesman in Tel Aviv said the tank that killed nine-year-old Alfnere had opened fire on Palestinian fighters who were firing rockets into Israel near the Gaza-Israel border.
"Israeli ground forces opened fire Wednesday morning on terrorists operating near Khan Yunis, around the security barrier," he said.
The incident occurred close to where Palestinian fighters fired 30 rockets into Israel on Tuesday, the Israeli military said.
A member of Hamas's armed wing and another Palestinian were killed in the same area, and later a fourth Palestinian was killed in a separate Israeli air raid.