Izzy seems small... Chloe came home at 9 weeks, weighing just over 13 lbs... At 6 weeks she was around 8 lbs... Still, at 9 weeks she slept a lot

Infact that's all she did... She even had me concerned... SHe's 16 weeks now - and just recently she has figured out how to play with her toys. She now has enough strength to make the squeekies squeek and to carry the larger toys around. When she was little she preffered smaller softer toys - and did not know - as she knows now - how to play by herself. I guess it all comes with time...
I am however surprised that she sleeps through the night - from 10 to 5 a.m.

... congratulations. With Chloe we got up twice every night (at 2:15 and 4:45 a.m.)... we also took her potty about every 2 hours during the day; just to teach her... Chloe also slept in a small crate at night (now she sleeps on a doggie bed next to me).
Do you take care of the puppy during the day? She can't be in a crate for too long - an hour at the most - but I'm no expert.
Chloe had 4 sets of shots - starting at 7 weeks - and finishing just recently - on Saturday. Thus, for the 6.5 weeks that she was home with us, she did not go anywhere other than our back yard, or the grandparents' yard... And was - and continues to be always supervised.
The first few weeks are though

but full of new love. Good luck with everything & have fun!