Rat vs the 2 yr old

Am I a terrible mother for laughing histerically at my 2 year old while she was being chased by a rat?

Deano is away tomorrow ( we have been waiting 2 years for him to get this job now he is finally off, I can hardly believe it!) So we thought we would go to the flying fox park in Baldivis and have a picnic. So Mat and Ali were going hard on the flying fox and I was playing follow the leader with Jaimiee ( guess who was the leader... NOT ME!) anyway this little hand bag dog/rat came skittering over it was only about 2 inchs' high.
 WELL!!! you would think a ROTwheeler had come to eat her up the way she quickly grabbed  my legs hugging them like her life depended on it, and hid behind me.  I bent over to give it a pat and
 was trying to encourage her to come and give her a pat, she had a lovely pink collar on and was nice and soft to touch. But nothing I could say was going to loosen that grip she had on that lard she was holding onto!
In the end Jaimiee took her chance, let go, and SPRINTED like she was going for the Olympic Gold. Well that was all the little rat wanted and it was OFF like a shot after her.
I saw the dog/rat owner, a lady in some fancy gym gear, come running after it as I also tried running after Jaimiee. At this point I had an image in my head of this being like a page in a hairy Mclary book!
I have to admit I was also a bit slow off the mark because it was also at this point that I dissolved into hysterics just at how ridiculous this was, which makes running not so easy.
Jaimiee eventually got down on the ground and curled up like a turtle, and I caught up to her, along with the fancy gym clothed lady, who was most apologetic. As I picked my little turtle off the ground I know that I should have been cross, because of 'what might have been' and the rat/dog was suppose to have been on a leash, there were signs everywhere stating that ( maybe RATS have an exemption!) but I honestly was laughing uncontrollably by this stage trying desparatly not to, as I didn't want Jaimiee to see me hysterical when she was frightened out of her mind by something that only came up to her ankles!
Later when we talked about it, I suggested that perhaps we could get a cat, for a pet but from the reaction I got I think she would have the same reaction, she is also scared of flys,ants,... and water on her head!
Perhaps I should start saving for therapy sessions for her now!