According to Mr.Nash his stack is just to big for it to be shove. If you consider things like his limping range and the probability that he's trapping it might be shove, but usually it's not, especially in a situation like this where you don't have much fold equity (which is a lot of what makes it worth shoving weaker hands in late game). 

I dont know if Q4 is push or not (its close imo) but aggr arguments looks bad or atleast have some kind of conflict. I assume and I am pretty sure that on 8BB game (400 donk stack, BB: 50) his limping range most of the time is weak. Occasionaly he can limp-call with hands like slowplayed monsters, K4 type hands etc. but most of the time he would shove/raise pf with any pair, any ace, big kings.a) if you dont have FE then Q4 is value shove vs his random hands like SC-s, JX type hands.b) if you have FE then his range is very weak and you are crushed vs his calling range but do not worry: you profit if he folds!In reality probably its between on two these extremes. In this kind of game your should have some kind of reads. If his button VPIP is high (like 70-80%), PFR is low (like 30-40%) then I think I would shove because most loose donks arent "balanced" and they raising range is TOP% hands and limping range very weak. So u have lots of FE.If his VPIP is low or most of the time he raise or you have punished his limps before then I think its better to check back because you are running into a monster a lot.