Welcome and congrats on the new rig!!!
The possible issue with the 150/1500 series is the payload. All passengers, cargo (coolers, firewood, bikes, etc), the wdh, AND the tt tw all count toward the rated payload that is stated on the yellow sticker n the drivers door jamb stating "All passengers and cargo not to exceed XXXXlbs". Any shopping you do you should look for this sticker on each vehicle you look at before deciding to but that exact one. The payload will vary from one vehicle to another based on options.
Another limitation is the tv receiver hitch rating. If I recall correctly the Burb is only rated for 1000lbs tw w/ a wdh. The "brochure" dry tw for your trailer is 780lbs which does not include the weight of the propane tanks or a battery on the tongue which will add ~120lbs to the "brochure" weight before you load the trailer up with anything additional for a trip.
Are you looking at a crew cab, 6.5' bed 150, or the 5.8" bed? Our Jayco 32 is about the same length, and the dry weight is a little heavier. Unless I absolutely had to there is no way I wound want to tow it with a 1500. I understand you have parking issues in regards to a crew cab 6.5' bed truck, but at ~8500lbs loaded, with maybe 1100lbs tw plus the family, plus any cargo in the bed you really are in 250/2500 territory. With that long of a trailer the longer the wheelbase the tv has the more stable the tow will be. Maybe a 150 w/ the tow package and HD payload package would be enough, but I don't know if that is available with the short bed.
The best thing to do before buying a new truck is to load up everything you will normally take, and with the whole family onboard go weigh your rig. Follow my signature link for the CAT Scale how to and make sure you get three seperate weights as described to figure all the weights of you rig setup.
Good luck!