I'm sorry but i agree with the girls, i don't see an issues with having a baptism in the same month as someone's baby is due.
To be quite honest there is no point planning it for BEFORE your bub is due as what if you go early? it's an EDD so theres no guarantee of a date for them to plan around.

You should do what YOU want for your own childs baptism, if you want small then have small it shouldn't be a competition with relatives and there should be no reason to be worried that it will be 'overshadowed'.
You might even like to do it around your mums birthday, like BG said people wouldn't have to travel twice and your mum might like sharing the month of her birth with her grandchild for that special reason.

I know sometimes the small things upset you, especially while your PG and you just want the best for your baby and want everyone to be happy BUT that said it is a small thing in the big scheme of things and your LO's special day will be special no matter what.

GL with it all.