I have a 19 month old and I am potty training her now (we started a month ago). Like your daughter she started imitating around 13 months old and showing signs of interest. Unless you are truly ready to jump in and go 100% I do not recommend starting until she is at least 18 months old and truly can begin to hold urine. It is amazing how frequently they pee! You will (even at 18 months) be taking her to the bathroom literally every 15 or 20 minutes for several days and STILL have plenty of accidents. In one day at the beginning we went through 10 pairs of underwear and still had 14 successful potty trips. They just pee a little bit frequently at this age.
It is a TON of work (every time I sit down to eat- my daughter quips "potty?" and we have to go. And if we are at a restraunt this will happen at least 3 or 4 times... then when I am in the stores- several times even though I just took her and she went or didn't- and now we are far from the potty... you still have to take them. As soon as I put her in the car seat "potty?". And when putting her to bed, about to lay her down (she wears a diaper at night, but if she says "potty" we go potty)... TRULY exhausting). I do recommend starting young while they are more interested- but brace yourself because it is tough. And make sure you have the needed supplies.
Good luck to you whatever you decide. We have to pick our battles and this is one we have to win, but potty training "ain't for sissies". I love the money we are saving, hate that my couch and carpet and daughters clothes (and mine too, oh and the poor cat- how did she manage that one?)smell of pee so often...
At 19 months my daughter does VERY well at home for the most part (not so well if she is tired)while she can run around naked, but not so great if she has people over and wears pants, or we are out and she is interested in things like a playground or friends.