Very jolly and cuddly for a baby but perhaps less suitable for an older child - however (as I'm always saying) nicknames evolve and often change once DC get to school.
If it matters, Theodora is usually spelled with a middle 'o'. It has a nice meaning (gift of god). The traditional nicknames include Dora and (eek!) Doreen. I prefer the English version of the name, Dorothea, rather than the shortened version, Thea, but Thea is a perfectly nice name.
Really like it, and I do like 'boy' names on girls! Really don't like Theodora though, it seems musty to me. But don't know what else it could be short for and agree Teddy probably needs a longer and more grown up option!
Love Thea and Theodora - Dora could be a lovely name if not for Dora the Explorer, though she's not quite at the height of popularity she was a few years back I think?
For the nn for a girl, I'd use Teddie rather than Teddy, just to differentiate from any boy Teddys. Obviously they sound the same but if you saw 'Teddie' written down you'd have a better idea that it was a girl and avoid any mistaken gender!
Love Theodora - it's my first choice if we have a girl. Just got to convince DH now although he loves the name Thea and he really likes the meaning as well so I'm hoping this will be easy! Really like Teddy as a nick name as well - hadn't thought of this.