Bottom line yes even a pump that say self priming can work "IF" and only if it setup under proper conditions. The laws of physics/motion/ nature will always win. Here an easy read on why setup placement is important :
https://blog.craneengineering.net/6-rea ... wont-primeAlso some that are called self priming when new do but if placed wrong will wear it out fast and no longevity to the filter and the weaker it gets will not self prime. You can make a pump last a full lifetime if setup under proper conditions.
I always thing safety first , my career was an inspector for the "NFPA" . Retired now and think safety even more today.
PS: most have a problem the other way , stands too high and a filter doesn't have the head pressure to get that high. People like us with tanks on the ground must watch placement . One of the best filter's is the FX6 with all it's hi tec circuity and purging // on page 7 it even has important note : NEVER install the filter above the water level ! Most reputable manufactures will state that. I use that filter for my on ground stock tank but water level at or above filter height to work. Bottomline the laws of physics will apply. There are ways to pipe things so to work as in industries but are involved and not cost effective to us. A couple cinder blocks under the plastic tub would be the easiest way to solve problem and cheapest. Get the water level above the filter.
Maybe an "in tank" filter system if your plastic tub is small with a baby but maintenance will be high. It also takes up swimming room. Just not enough media area with them , I don't really recommend them but works with very low water levels .
Do you have any dollar stores in your area , since it's a plastic tub / tote type you have get one with taller sides so to add more water and use filter you have already. Even baby turtles swim great it's a born / natural instinct to them.