It very rare indeed for a security agent to called a friend over to have a laugh. Border agents see something like one person per minute when they work at inspecting passports. That is close to 100,000 photographs each per annum. Would a friend be called over to have a laugh at something that happened to the border agent every week? I suspect not, but maybe once a month – less often if there are several agents sharing such jokes (it is only amusing if out of the ordinary).
On the other hand, presumably someone responsible has certified it was a true likeness, so maybe odd but nevertheless adequately recognisable. And if it is good enough for the people who issued your passport then no Israeli can object to the photograph (though they may not let you cross their border with it).
It is also very rare indeed for passport photographs for adults to cause issues (once accepted for passport use). However Israel can be expected to be more sensitive than most about identification, both because of their general security situation and for what they themselves are believed to have been up to, for example the 2004 Israel–New Zealand passport scandal and more recently the assassination of Mahmoud Al-Mabhouh.
If you were to 'renew' now you would be getting only six year's use of a ten year passport. Four years' share of the current adult ten-year renewal fee of AUD 254 is around AUD 100 (around US$ 75).
If you are really not too bothered about being allowed to enter, then save $100 and take the risk. Even if entry makes quite a big difference, still take the risk as it is not so much of being refused entry but having to waste some time with additional questioning and checks - if that.
If entry makes a very big difference and the photograph is as unrepresentative as you seem to imply, then buy a new passport, or you will be uncomfortable all the time until you arrive in Israel. Perhaps console yourself that all you are wasting 'now' could easily be what you would otherwise have wasted in the future.