I'm a Dad of a DD who did Rainbows for a year and went up to Brownies (which she loves) with a couple of girls her age. Rainbows was OK but honestly I would say Beavers is far better and offers a lot more in terms of what kids can actually get out of it. Rainbows is about singing together, sticking and glueing, doing fairly "girly" stuff and learning the basics of team effort and the scouting "ethos" which is all great - but might be a bit basic if your DD is at the upper end of the age bracket. DS2 (5) started Beavers last year and it's fab. A "proper" uniform with a jumper, scarf, woggle etc, (which can kind of matter at that age), small camps (a one night sleepover), outings, group/team stuff out of the hut and in the world - it's all good.
The hut happens to be opposite a huge park and actually I'd say that should be a major consideration in your decision because exactly WHERE the hut/base is can make a HUUUUUGE difference to what beavers / brownies / cubs / scouts can regularly and easily get up to week after week and therefore the experience that kids have when they attend. We live in the city so camping / fire lighting / fishing etc is not easily on the agenda but Beavers / Scouts is making it possible for my kids and it's great. So I'd advise to choose a group which has easy access to a park or large green space and which can also offer scouting "all the way" i.e. from beavers to cubs to scouts or rainbows to brownies to guides so they can stay involved if they want to in the same group in the same place with continuity year after year.
If you don't mind about all girls / all boys / mixed then I'd say go straight for Beavers if you think she'll cope well and be welcomed by the (mostly boys?) who are already there and who are probably older. But check it out well because what you don't want is a day one shocker that puts her off forever.
My experience of Beavers on day one was that it was pretty boisterous, very loud and full of manic boys screaming about the place ! On arrival my (usually very confident) 5 year old went for a five minute leg cling before he'd go it alone and get involved.
One more point is that I wanted my kids to go into something away from their school and from their school friends but near enough to home so that the friends they made could still be local and easy enough to visit. This has turned out to be very valuable as they have gone on through school. It's good for them to have "other" friends, away from school (especially senior school) when things get tough, stuff happens (as it always does) etc etc...
Overview: check out all the local groups before you decide - the nearest one is not necessarily the one you want - one Rainbows might be better than the other Beavers simply because of location or the personnel or vica verca - and your DH might have a point about Rainbows - there's no hurry to grow up !