Well, the situation is that Israel has secured enough vaccine/vac commitments for its population. And more, since they pre-ordered not knowing which vaccines would work or when they would be ready.
I doubt Jordan is in such a position. Most likely they are left scrambling for Russian or Chinese vaccine. [Edit: Jordan has 1M doses of Pfizer's vac; 2M more on order via the WHO program; and a lot of China's Sinovac coming in] Jordan is vaccinating anyone in the country for free, including nearly 1M Palestinian refugees there.
Jordan also has perhaps 1M Syrian refugees. Jordan has the highest % of refugees -- 7M Jordanian citizens and 2.5M Syrians and Palestinians. Basically Jordan is already doing more than its share of assisting stateless people.
Things were looking up slightly for Gaza when Mubarek was overthrown and the Muslim Brotherhood won elections. Shortlived, as the elected gov't was soon overthrown in a military coup bringing back the exact same corrupt, anti-democratic, anti-Palestinian forces in Egypt. They've had trouble controlling the Sinai, so have no interest in engaging with Gaza.
Egypt has 100M people, so it's going to take some time for them to get enough vaccine and distribute it. If Palestinians look abroad for help, they have good UN connections (and are expecting 2M promised Pfizer doses from WHO), Qatar is rich and actually assists Palestine with funding; Turkey and Iran are allies, but have large populations to contend with. Of course if Palestinians had their own country they'd be in a much better position to help themselves. And the history of saying Jordan should deal with Palestinian needs is often tied to a denial of Palestinian land claims and/or a denial that Palestinians are a separate people.
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