I am single, in Israel, with a baby, with no father registered on the birth certificate. Can I get an Israeli court order to carry out DNA testing on the "father" even if he lives abroad?

Yes - this is possible! Special procedures exist for obtaining DNA samples for the purposes of paternity proceedings in Israel if the alleged father is overseas.

Paternity testing in Israel is only carried out following a court order and because you are single there should be no bar to performing the test.