My good friend is due mid-June. She has had a pretty rough pregnancy and was just put on bed rest.
I'm thinking that now the easiest thing for her would be to take the baby shower I planned to have at my house and have it at her house instead.
Or maybe I should just postpone it until after the baby arrives?

No, I would take it to her. It's likely that right now she feels horrible. She'll be lonely and miserable and a shower, with lots of little baby gifts could do wonders for her mood.

It will make more work for you but definitely go to her. She will thank you a million times over for it!
I would suggest going over the day before to do some house cleaning and decorating. That way everything is ready for the shower and all you have to do is show up with the food.

I think that would be a very nice picker upper. I agree about the cleaning suggestions, because things are bound to be out of place, and instead of feeling happy friends are there she may start feeling bad about the various things are undone.

I would know many that would love this happen, having the shower come to them could indeed lift spirits up. I have been on bedrest before and it is so boring, if I could share a shower even being stuck in bed I would!

Give it to her now. She's probably very lonely and would love the attention. It will get her mind off the bedrest, at least for a few hours. And don't forget to bring something for her too.