A border collie???lol (It sounds like the last thing you need is a hyperactive dog.)
I find our life is much easier when we have places to go and friends to play with. We have two kids and although that does increase the workload, at least our kids have an always available playmate.
I babysat a couple days a week (and didn't charge for it) just so my son would have a same age playmate. She is starting school now so we'll see how that relationship transitions.
We try to get together with homeschooling kids as much as possible. I eventually figured out that, for our family, building relationships with kids who will go to school means those relationship have an end date as their time to get together gets limited and tends to be the time we reserve for family time. Not 100% true, but as these kids are getting closer to school age I see that happening.
I don't believe in overscheduling, so I try to only schedule one event a day. Monday is a craft class through parks 'n rec, Tuesday is homeschooling park day, Thursday is another homeschooling gathering, Friday is storytime at the library. There is plenty of opportunities for play before and after all these events, but it really helps to just get out of the house. We also have a membership to the children's museum, botanical gardens, etc. Places the kids can explore and spin their wheels.
In the evenings we go swimming as a family or go for walks. Again, getting out of the house.
When our little one is napping, our son gets screen time. Right now he is watching a documentary about airplanes. He gets to watch documentaries or youtube--educational stuff. He likes How It's Made. For quite awhile he liked Betty Crocker cake decorating stuff, but that seems to have gone by the wayside. He's 5.5 and really talks about what he is learning--the physics of flying, the propellers on a helicopter, how to cut an avocado. Today we spent a long time reading through a children's encyclopedia together. We were reading about different kinds of machines. It's amazing to see how all of a sudden he seems to be craving learning about stuff. No indications he wants to read, but he wants facts.
At this age, I think the most important thing a child can do is play. Read "Einstein Never Used Flashcards." http://www.amazon.com/Einstein-Never-Used-Flashcards-Learn--/dp/1594860688/ref=sr_1_1?ie=UTF8&qid=1309119559&sr=8-1
Or read this article by Harvard professors on the importance of play: http://www.cnn.com/2010/OPINION/12/29/christakis.play.children.learning/index.html
So, playdates, playdates, playdates.
Plus arrange a bunch of really cool homeschooling field trips. Recently we toured a solar installers, a hydroponic research garden, the optics dept. at the university, etc.
And have LOTS of books about different subjects available. Either buy used or get from the library. I never know what or when my son will want to read. The encyclopedia he was reading today was someone else's throw out. We must have read it for 45 minutes. Because he wanted to.