I don't think you can travel on your proposed itinerary.
Entry to the UAE is not permitted for Israeli passport holders. You can only transit airside if you are traveling with an Israeli passport and have no other passport.
If you attempt to board the first flight, the airline will tell you that a visa is required or that you will be refused entry to the UAE, and will deny boarding on that basis.
If you have a passport from some other country, you may be able to use it to transit landside.
You might be able to pay marhaba to transfer your bags for you, but that doesn't eliminate the problem of being denied boarding in the first place.
If the two airlines have a baggage interlining agreement (almost, but not quite the same as, being in the same alliance), you may be able to convince the check-in agent to through-check the bags. He or she may be unwilling or unable to do this, though, when you have separate tickets.
If you want to be assured of making this connection, you should buy the entire itinerary on a single ticket, rather than separate tickets. In this case, the airline will through-check your bags (with very rare exceptions). If you actually did buy a single ticket, you may be confused and think you need to transfer your bags yourself, when you actually don't. Check with the ticketing airline in this case to find out what will happen.