K.N.
Yeah, my daughter is 38 months... She still has a tendency to count "the Enron way" (LOL!) although she tends to do it more now when she gets between 15-20.
At your daughter's age, she is still rote counting, meaning her focus is on sequential order and verbalizing/remembering what number comes next. Applying each number to a specific item (and then instantly remembering which number was assigned to that item) is a much more advanced milestone.
It might be easier for her to understand counting and number assignment if the items are tangible (and she can hold the ones she has already counted) instead of applying numbers to a picture. However, keep in mind that at 18-30 months, her brain is primarily wiring itself for gross motor skills and fine motor skills: Coordination, balance, being able to move different parts (e.g., left leg, right arm) of her body simultaneously in opposite ways, target and aiming. Now is the time to increase your attention and efforts to motor skill milestones.
Below are some links. Hope they help plan your strategy better:
http://www.meddybemps.com/7.26.html
http://en.wikipedia.org/wiki/Child_development_stages#Two...
http://en.wikipedia.org/wiki/Child_development_stages
From http://www.gdrc.org/kmgmt/learning/child-learn.html:
Math skills: These skills develop with much practice and we encourage their development as the child is ready.The child begins to count for fun (rote counting). Then they begin to see the purpose for counting and begin counting objects in a set (meaningful counting). Next they begin adding to or subtracting objects from a set. They begin comparing objects in a set. Then the child begins sorting (by size, shape, color, etc.) and ordering (by size, first-second-third, etc). They enjoy learning to estimate (guess how many) and predict (what will happen next). They begin to sequence objects (red, yellow, blue, red, yellow, ____). This is a slow process and requires a lot of practice. At last the child begins to recognize numbers and associate the number with a like number of objects. They also begin to write numbers. Later, they will write the number words. If we make this learning fun, children will enjoy learning math through their school years.