It's impossible to give you any kind of certainty, but according to what you have said to us, she does appear very interested. Women are the masters (or should that be mistresses?) of over / understatement. Assuming she isn't blind, she certainly knows that YOU are interested. If she wasn't interested then it's fairly certain that she'd have given you buffering signals (no I don't mean the noise your modem makes) at some point or plain chosen another park to walk her dogs in.
At the end of the day you can ask the advice of every person on this forum and still be left no definitive answer to your question. The only person who knows the answer is the woman you're interested in!
If you are nervous then I would second the advice of others who suggested moving things forward from meeting with your pets to an actual proper meeting whether at a neutral place or one of your places. One thing I can pretty much guarantee though, if you smile and ask her if she'd like to go for a cuppa sometime and she says yes, she isn't doing it because she's looking forward to a nice hot cup of earl grey... more likely she wants to get to know you better (whatever that entails).
Carpe diem
good luck!