Close to square is close enough for turning in my book. I've turned stuff out of almost triangular sticks split out of a log with an axe. If you need it square to register lips, eyes and bellyholes, you can probably get it close enough by tablesaw or bandsaw with a fence...
If you "need" a planer I can't offer any suggestions because my only experience is with a 12" Ryobi that does an OK job..
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