I so hate that title of "older mom!" Yes, I had a child a little later in life then some, and hopefully she'll have a sibling sometime in the future, but I don't believe it is harder. I have to chase her around all over the place, just like friends of mine did back when they had their kids, but I truly don't see the difference. I keep up with her just fine. We have the same "issues" that all moms have. In the past couple of days "we" (and in the term of we, I mean her), have eaten a handful of tums and some diaper rash cream. Would she not have done that if I was 15 years younger? I doubt it because kids are kids.
As for the puppy issue, we have put that on hold for the time being. I want to wait until she is a little bit older so that she understands that a pet is not a chew toy or a stuffed animal to sit on or throw, or pull its tail. I'm sure my 18 year old cat hopes that she realizes that really soon.