There's no reason to make a trade with Washington because in all likelihood, Washington wouldn't even consider drafting Quinn because they just spent a 1st round pick on Jason Campbell. They started Campbell at the end of the year, he's their QB of the future. Plus, the Skins don't have a pick after the first round until the fifth round, they can't afford to use their first round pick on a guy that would be on the bench. The lack of Day 1 picks is why the Skins are trying to trade down.
Look objectively at the QB situations for each of the teams above Miami in the draft:
1) Oakland - probably will take Russell or Quinn, current starter is either Aaron Brooks or Andrew Walter
2) Detroit - Kitna threw a bunch of picks but also had over 4000 yards this year, he is getting up there in age. A QB could get taken to sit for a year or two, but they have a lot of other holes on that team.
3) Cleveland - Charlie Frye and Derek Anderson started games for the Browns this year. The Browns seem to like Frye a good deal, but I think they would look hard at Quinn for his potential, and for 2 other reasons. First, he's an Ohio guy, and second, Crennel is the coach there and you know that he'll get all of the info on Quinn from Weis since both of those coaches know each other from their Patriots days.
4) Tampa Bay - Chris Simms just signed a 2 year extension, but Gruden could get excited about a QB if Quinn or Russell is still there.
5) Arizona - Leinart got taken in the 1st round last year, almost no chance they take another QB.
6) Washington - see above
7) Minnesota - spent a second round pick last year on Tarvaris Jackson, and will probably go into next year with him as the starter since he ended the season as the starter. Little chance they'll take a QB again.
8) Houston - David Carr is still the starter for now, rumors are flying that he may be let go, but rumors are also out there that Gary Kubiak will get reunited with Jake Plummer in Houston. We should know a lot more after the free agency period.
So out of the 8 teams that pick ahead of the Dolphins, I think that the top 3 teams are the teams with the highest likelihood of picking a QB. However, it's easy to see Detroit and Cleveland going in directions other than drafting a QB, so if you look at it, Quinn could be there as #9. If he's there and the Dolphins don't want him, they should look at teams in the 10-20 range that may be in search of a QB. The problem with that line of thinking in this: barely any team in the 10-20 range is unsettled at the QB position! Look at it:
10) Atlanta - Vick and Schaub
11) San Francisco - Alex Smith
12) Buffalo - JP Losman played a lot better last year, I think the Bills will stay with him
13) St. Louis - Bulger
14) Carolina - Delhomme is the starter, but they could maybe look at Quinn if he was still there
15) Pittsburgh - Roethlisberger
16) Green Bay - Favre for at least 1 more year, then Aaron Rodgers
17) Jacksonville - Garrard was the starter at the end of the year and may go into next year as the starter with Leftwich traded, both are under contract right now, so no need to draft a QB
18) Cincinnati - Carson Palmer
19) Tennessee - Vince Young
20) New York Giants - Eli Manning
So looking at all of this, I could see a fall for Brady Quinn like what happened to Aaron Rodgers a couple of years ago if teams draft more on needs in the first round as opposed to drafting best player available. As far as Quinn, I wouldn't mind the Dolphins taking him to develop for a couple of years behind Daunte. If Weis says that he'll be really good in the NFL, that's good enough for me.