Of course you can hold someone else's baby while you're on your period.
Menstruation does not stop you from doing anything that you would do normally. There are many myths surrounding menstruation and what people can do while menstruating, but they're all just that - myths. A menstruating person cannot harm anyone or any thing on her period.
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Why couldn't you? I'm not sure what you think is going to happen, but menstruation has nothing to do with holding babies.