I'm really sorry this happened and I hope both you and your toddler are ok.
First of all, what you have is a young cockerel - not a rooster. Also, culling just means to remove from the flock (or sometimes even just from the breeding pool) but since you also mention rehoming I'm guessing you're asking if you should kill him.
Killing him is definitely one option. It'll be the quickest way to get rid of him and could also provide you with a meal if you're comfortable doing that. Rehoming may also be an option, depending on where you live and whether you'd be comfortable with someone else taking him to eat. If you have a local Facebook page or something other website people use for local advertising, that's probably the best place to start. Do make it clear why you're looking to rehome him.
While his sex may well have been a factor in the behaviour, pullets and hens are also plenty capable of injuring a small child if they're allowed to interact without close supervision. It doesn't even have to be intentional; just one curious peck to the eye could be enough. I'm not saying this as a criticism or judgement of your parenting but please keep this in mind in future.
I also don't agree that this is a sure sign he's going to grow into a human-aggressive monster of a rooster. It's hard to comment or form an opinion without knowing much more about what happened but I think it's worth pointing out that he's right at the age now where they often turn into hormonal idiots for a while - and he doesn't have any older flock members to keep him in check or teach him the ropes. If you're fairly new to chickens then this could also seem like an "unprovoked" action because you just didn't recognise a warning sign, and toddlers are too young to even learn to read an animal's behaviour and body language well until they're older.