Not to buy my almost 1 year old a sun protection swim suit thing?

[Ramekin]

We have a lake near us that is great for outdoor swimming in the summer.
DD (4) loves splashing about in freezing water outside. Last year she didn't have a proper "sun protection" outfit, so I made her keep her T-shirt on. This year I have got a the proper SPF 50 lycra suit thing (or whatever it is they are made of).

I haven't got anything for DD2 (nearly 1 yo); my thinking is that she isn't going to be swimming as such, we'll probably take her in to splash her toes for a few minutes, but it's going to be too cold for full body immersion, so it makes more sense to dress her in swim nappy and cheap T-shirt, which is easier to strip off if it gets wet than a full sun protection suit.

Everyone I have mentioned this to has been aghast, and said I need to get her proper sun protection . But surely a cotton t-shirt will be just as good if she is not actually going in the water much?

The thing I don't get about sun suits is why they are short-sleeved/short legged - I mean, don't forearms and legs get exposed if it's so important to reduce exposure for long periods? Or am I just being a bit thick

Both my dc have them, always put sun cream on first.

We get the Radicool ones. I think they're Australian...