"Tiiiiiiiiiny doubles..." - you know, I can still hear Don Ho singing that song at the Hilton Hawaiian Village.
Figure out how much gas you need - then find the rig. You're small - you'd look like a munchkin next to me. THE best tanks I ever saw for smaller women are the venerable LP66 tanks judiciously overfilled. Oh wait... that's not allowed anymore.
Even filled normally, there's probably enough gas in one of those little puppies to let you outlast all the hosses diving with you.
I can carry giant pieces of furniture - it also means that I use a LOT of gas on a dive. Time after time after time, I've seen these leetle itty bitty women with a toy LP66 outlast me.
Now that said, twinned LP45's are about the coolest little set of doubles out there. LP85's start getting heavy. I have a set, and they are pretty snazzy, but it's been years since I used them. I just go with my HP120's that replaces my LP 125's that I ran at 4500psi. I had twin AL 80's a long, long time ago - they were ok. I like the steel weights better.
So you have lots of options...just try not to buy 'em twice getting it all right.
The RB is another path to trot. It can be a little pricey, and you can't harvest lobsters in Floriduh on one. You'll figure it out.