Parties after school on weekdays, I don't see why not.
To answer your question about invites, I usually send them out 3-4 weeks before hand and I insist on RSVP's. I then follow up the week before the party just to see if they can still make it, etc. You could probably do it 2 weeks before though, too. Just keep in mind that some parents may have already made plans and wished that they'd known about the party sooner.
As for sending them to school, I wouldn't do that. Unless she's inviting the whole class it causes too many hurt feelings and mis-understandings. Either help your daughter hand deliver the invites to the guests homes, or send out invites by email. I always design my own invites on my computer and then email some to those that liver further away (such as family members that can't make it but want to be remembered) and then print & hand deliver to those that lived closer. My children's school actually has a policy that no bday party invites are to be handed out at school unless the whole class is invited.
As for having the party after the fact, you certainly can. And with you having a big arrival coming up, you shouldn't exert yourself over a bday party. I would have a small party just for family on the big day. A nice cake and maybe a gift or two. Then, a month or so later, have the big party with all the friends and stuff. I've had to do that a couple of times and as long as I made a big deal of it on their big day, my kids didn't mind. I have two children with bdays within a week of each other (4 years apart) and last year at that same time we were moving. They each had a cake on their day but we wound up not having a party until 2 months later. We had a big thing at the park and wound up celebrating not only their birthdays but my husbands bday (this wound up being ON his big day LOL) and when my brother came down with his little guy we added him too because we wouldn't see him the next month for his bday. :D Also my youngest son was born the day after Thanksgiving. There is no way I'm giving him a big party with Christmas so close etc. We're planning a trip to the arcade later this month for him and some buddies. There is a friend of mine that has two boys and they were both born in December. She didn't feel like doing X-mas & two parties so she does something similar. On their day, they each get a cake but no gifts. In June she throws a huge party for the two of them and they get their gifts then.
So relax. Stop worrying about all of this and focus on taking care of the little one. Making your daughter feel special on her big day is what's important. Not throwing a huge party and just stressing yourself out in the process.