Hi tleray
A very warm welcome to the Camera Labs forum.
You have no doubt already seen Gordon's
best super-zoom digital cameras buyer's guide as well as his
Olympus SP 550 Ultra Zoom review. I see that your A80 has an equivalent 38-114 mm optical zoom. If you are happy with the wide-angle capabilities of this camera then you have a pretty good choice of "super-zoom" cameras. If you want a wider angle then at first glance it looks like the Olympus SP 560 Ultra Zoom with its 27-486mm zoom may be worth the wait.
Have you a firm maximum budget in mind? Pretty likely with a new baby in the house I guess - congratulations by the way! I am not going to point you towards the world of DSLRs because I don't think that's where you want to go right now but for fun why not have a look at Gordon's
Canon PowerShot G9 review? You may well not be tempted (but it
is a Canon and you currently
are a Canon owner

) but perhaps you would value the compactness of this camera (very easy to have it close at hand for those baby photos) compared to a more bulky super-zoom. It has a proper flash hot shoe as well as built in flash for those indoor photos. If you haven't ruled out a compact form factor from your upgrade then you might want to check out the
best compact digital cameras feature on this site.
Good luck with your decision. Let us know how you get on.
Bob.