Its fine. With 1.5 times potsize left you arent EVER folding. Youll get called by KK,QQ,AQ (if he has it),AhKh (if he has it)
even just taking his range as KK,QQ,AA you are ahead since he has KK more often than QQ (because one of the Qs is out). Also any other hand that he might have is behind you.
Having said that it might be better to bet say $0.70 and then push the river. This is really opponent dependent though and purely depends on which you think hes most likely to call with JJ.