If she were my puppy, it would depend on how many sets of shots she's had (sorry, I can't remember the schedule). Also, I would ask the groomer if she can assure you that any dogs coming over are up-to-date on their shots. I do not think that she's too young to be groomed. I think the earlier you start the better. It's easier to get a puppy used to new things than an older dog.
I also think it's good to socialize your puppy with other animals & people as soon as it's safe. I did not do this and am now having problems. To correct the situation, I've had to spend three times as much time trying to "upset the apple cart" (as someone said to me). Instead of spending time cooking dinner, I'm finding places to go where I can bring my puppy - no complaints here
my kids are loving it and I'm loving spending so much time with Lexi.
This is just my opinion. There are many on this board that are ALOT more knowledgable than me. I'm sure you'll get more advice. Good Luck.