Dude..Your day one itinerary is fully loaded, i doubt if you could cover all of them without having to rush from one place to other...
from my experience in my vist to kashmir last sept....
Travel:
1.Travelling to srinangar from jammu or somewhere else (to and Fro) by air is much better than by road.( if you could book early By air ) you will reach srinagar in like 1 hour by air while the road NH1 will take you around 7-8 hours depending on the traffic and road blockages. Heavy trucks, narrow road with shepherds blocking traffic is very frequent. the road is very treacherous. the innova would be a cheaper option. compare flight rates with taxi rates. the approx innova would cost you around 6k - 7k.
2. Hire taxis with reference , there are a lot of references on the tripadvisor forum, save these numbers as they might come in handy. also when i booked taxis with these references. There are taxi stands around dal lake and srinagar, even though the prices are fixed, i found them a little expensive. i got much better deals with those references on trip advisor.
3.as rightly said by @ peppes3484 ...when visiting a certain place like gulmarg or sonamarg. once the taxi reaches the spot. you have to take a different taxi/ pony rides to go to the main points. these taxi wallahs and pony wallahs will charge you exorbitant prices and try to justify it. they are also very aggressive, stay calm and bargain, roam around and research a bit by talking to other tourists. they will guide you well! for a trip worth 300-500 they will charge you 2000-3000-4000!
about the itinerary:
1. if you are gonna stay at a houseboat and want to vist sightseeing, i recommend at dal lake. nigeen lake is a bit isolated, there is no way you are gonna cover all the lakes/ garden + sinthan top all in 1 day. Dal lake and nageen lake are close by even all the gardens/ temples/mosque are all around dal lake, each of them at a distance of 5-10 mins. also the gardens are big enough to consume a lot of your time. In my opinion, try spending less time at the gardens/temple/mosque and more time for Shikara rides.. i found them as a much pleasurable experience. i wanted to do them more and more. while i was getting bored at gardens

also the taxiwallah at the end of your day tour will try to take you to a carpet factory...as i am asuming they get commisions from them. dont waste your time there unless you are interested in buying kashmiri carpets.
2. Sonamarg is very very very beautifull - especially the galcier/ the road / this will take around 5-6 hours, do not skip this at any cost, try to spend most of your time at the glacier, its heavenly .also dont miss visiting apple orchards on the way. as it is apple season in sept/oct.
3. before reaching gulmarg the taxi wallah will try to stop for you to rent clothes like jackets/snowboots at a store. avoid this unless you really feel its very cold. also the taxi wallah will park at a stand and from there you will have to goto the gondola ride. threre are pony wallahs who will persuade you to take ponies, its a 10 min walk to the gondola. skip taking ponies unless you feel that you cant walk 10 mins. Gulmarg is very beautiful and is an experience especially the second phase.
4. you can do sinthan top today if you want to..or just realax in a shikara ride.I doubt if the tulip garden will be open in oct.
5&6. Pahalgam is very very beautiful...staying here for 2 days is justified. escpecially aru valley. you will find a proper hotel at the topwith tablesand chairs in the lawn, have kahwa here. its simply heaven. lidder is located right in between pahalgam. you will need heavy woollens here. coz even in sept the temp reached -5 at night. Try to get a hotel near the main market.
Final Notes: Kashmir is a very touristy place, most of the households here depend on tourists hence. Bargain hard, dont give in too fast. Also avoid argument with taxi or ponywallahs, they are very aggressive if complain or crib about their services. but dont fear them..stay calm and try to get your way with them. Also hotels here are expensive, refer tripadvisor for options and bookem online if you get a very good bargain. you could save a lot of money here if you research wisely. Try to get a hotel near dal lake. there are many hotels at reasonable rates in the back lane of dal lake, just 2 mins from there. only postpaid works there.
Have a great trip!! it is sure to be one of the most memorable trips of your life. i was a little skeptical at first, but even in todays time Kashmir is truely heaven on earth.