Advice for lower power clock type project Arduino newbie here! I'm a programmer but my hardware knowledge is ... slim.

I'd like to build a clock type wake up timer for my daughter, using an Arduino type board. Probably overkill, but it's practice for me, not just the end result! The idea is that is sleeps all night, then around say 4, gradually fade on a red LED. At 6, which is when she's allowed to come in, the red LED switches to a green, or some colourful sequence that tells her it's time. At a later time, maybe 7/8, it goes back to sleep to conserve power.

I have an Arduino Uno, but looks like I'll also need an RTC, and I've read that the sleep power consumption is ~40mA, which on batteries is what? A day or two max?

So I'm thinking I can't do this with a Uno.

So, my question is, are there any very low power Arduino compatible boards with built in RTCs that I can use for this project that will get me up and running as quickly as if I was using the Uno?
I will make my comment an answer:
Try one of Arduino supported RTC's boards. The most popular (and simple) are: DS1302, DS1307, PCF8563, and - very nice, precise DS3231 (my fav). Hook any of them up to your Arduino, add some (readily available) libraries, tweak a little and voila. The RTC will work from coin battery (or high capacity capacitor called supercapacitor, like this one)  

Most (if not all) of mentioned RTC have 'alarm' function: you can set up your system to wake up your Arduino from sleep (sleep state to save battery) and gradually light up the LED. 

To limit current of Arduino try removing LED, or - better - try to use Arduino Pro Mini. To modify it for better power saving see here  

EDIT:
There are some other low-power boards:
Moteino
Rocket Scream Mini Ultra
JeeLink  

Also, (as mentioned in one of comments) you can try one of ESP8266 and push it to one of many sleep modes. Try this link.