I've spent many many hours at Abbots Quay; I worked at/ran the boat hire there from about 1980 to 1990...
The slip is very narrow, and the road to the front of it is also narrow, athough you can use the stone paved quay area to set up on. Then you'd have to find somewhere to park your car and trailer; I've not looked at parking there for years (although have walked that area on trips back to see family). There may be on street in Pound Lane if you are lucky, or the Streche Road car park was the other option (although I think the spaces there are now more fomalised than they used to be).
How about launching at Ridge Wharf; you could then travel up stream to Wareham, stop at the main Quay and then continue upstream further. Wareham would be a nice place to stop for a coffee or beer (we had a great Sunday Roast at the Kings Arms in North Street when we were last back).
We used to let the boats with outboards go up about 3/4 mile beyond the Quay. After that the weed would get dense and you'd need to keep stopping to clean your prop (and keep your cooling). However, as it is your own boat and if you pick your way you may make it further. The railway bridge (Swanage line) is from memory about 1.5 miles. I think the river is tidal that far up (and therefore legally navigable??). However, it was all a long time ago and it was about 10 years ago that I last went up the river.
http://www.ridgewharf.co.uk/services