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Actually you want a thinner consistency icing for a buttercream transfer, one that will flow easily. So if you thickened it up, it will not flow well and will be more difficult to smooth.
I use 1/2 cup butter
1/2 cups shortening
1 1/2 tsp. vanilla
2 cups of icing sugar
I beat the butter on low until completely softened and add the shortening, again on low. Then I add the vanilla on low. Then I add the icing sugar.
The other thing I do differently, is I let the completed transfer sit for about 25 minutes, then sprinkle some icing sugar on top, then press down vertically, actually a gentle pouncing motion, to get rid of any squiggle worm effect until smooth. Then I put the final coat of icing on top, again wait the 25 minutes and sprinkle on more icining sugar and smooth with fingers again vertically down. Then I carefully smooth over with a spatula. then I sprinkle a bit more icing sugar on top, cover it with parchment paper and bag the whole thing, glass and all and freeze. I tend to freeze these overnight for up to two weeks.
If this is your first transfer and you are not sure of what consistency you need the icing to be, I would suggest you try this recipe. It is exactly the right consistency. Once you know that, you can use Dawn's or anyone elses buttercream and thin it down so it is like this consistency. Just a suggestion.