Yes, of course, totally fine. GF routine would say 2 hours of awake (so nap at 9am after a 7am wake up) but I found both of my girls wanted to nap earlier and I always just put them down when they started getting fretty. Excellent timing to dive in the shower, eat some toast and stick a wash on in my view!
Yes definitely. It took me ages to realise that dd needed a nap so quickly in the morning! It felt like she'd only just woken up and I was putting her down again, but they do get tired so quickly at that age. I think lots of my early napping problem were because I didn't recognise this sooner and she got overtired and then couldn't sleep.
Blushing I did exactly the same first time round! You can't quite believe that they're tired again an hour after getting up when all they've done is feed, burp, have a nappy change, sat in bouncer for five minutes!