I think you, or anyone with some life experience and solid common sense, can sail although I would encourage you to save a little more money so you can buy a good solid boat with reliable systems in place.
My husband and I have only been sailing for 6 years but we are leaving this fall from Florida to the Bahamas and can hardly wait to begin our "live aboard" life.
We taught ourselves to sail our 29.5 Hunter without a great deal of risk to life and limb and would suggest that patience, weather suitable to your skill level and a good solid knowledge and understanding of charts and navigation then sail, sail, sail! Here, there, everywhere!!! Life will happen and you and your gf will need to respond to it.
There are many books written about individuals who have walked down to the dock one day, bought a boat and left for parts unknown with great success.
I expect you have already done some sailing in heavy seas and have decided this is a life that could work for you and your gf....if so, I say go for it and I hope we see you along the way. Btw, your pet is not a problem as long as all vaccines and good health are vet checked and confirmed, lots of cruisers have furry family
Cheers and happy sailing!