You can do a front facing out (FFO) carry in a wrap. However, it will be less comfortable for both you and your DD than front facing in or a back carry. There are a couple of main reasons:
If you carry your DD FFI, the fabric of the wrap can be spread from knee to knee - she should be sitting in the sling with her weight fully spread across her bottom and both thighs (bum lower than knees). For that to work, her legs need to wrap around your body. If you carry her FFO her hips just won't bend the right way and so the fabric of the sling will need to bunch between her legs and all her weight will be on her crotch.
Its much easier carrying a weight that's leaning into you rather than one that's pulling away - a child's centre of gravity is such that their weight pulls them forward - so FFI gravity pulls them in closer but FFO gravity is pulling them away all the time. You back will suffer much more quickly if you carry a large child FFO.
DD has just turned 2. I've never carried her FFO and she's always managed to see what she wanted (I'd stand sideways sometimes to make it easier). If she was tired she'd also rest her head on my chest and relax. I still carry her on my back (either wrap or MT), but carried her FFI until a couple of months back. I don't know whether the over-stimulation thing is true or not, but I felt that at least I was giving DD the option. And I liked the cuddles .
Have you used a wrap before? I started with a stretchy wrap when DD was 2-3 months, and the stretch made it very forgiving - but it was starting to strugle with her weight by the time she was about 7 months and I now have a woven wrap and a couple of MTs. A MT probably has a smaller learning curve than a wrap, but a wrap is more versatile once you've got to grips with it. DD prefers the wrap to the MT at the moment, but that changes from time to time.
Have you come across slingmeet? If you could find a group near you you'd be able to get some real life opinions and should be able to give a couple of wraps and MTs a try. Would you consider buying 2nd hand? You can get some absolute bargains that way and if it doesn't work out for you you shouldn't loose much (if anything) selling it on - the UKbabywearingSWAP mailgroup and the naturalmamas forum are both UK based and worth looking at.