I am constantly worried that my 13 month old daughter is not eating
the right foods and I worry she is not eating enough. Also, How much
milk and plain water should she have each day? Can you provide a
detailed sample menu,or a link to one, so I can go from that? She was
born 4 weeks early so should we add an extra month on to any
developmental expectations? She isn't walking yet but she will stand
and hold on to furniture.

See prior similar question.

http://answers.google.com/answers/threadview?id=548856
Q: 12 month old baby - dietary, sleep and exercise requirements

Perhaps a couple of good books on toddler care and health would be useful.
Don't get too many; they won't all agree, and you could just feel confused. 
Dr. Spock "raised" a couple of generations of children.

http://www.amazon.com/exec/obidos/tg/detail/-/0671537628/103-8674283-2599804?v=glance

Being born 4 weeks early should not be a concern at this stage.
When assessing growth,consideration is given for prematurity up until
One year of age,but not afterwards.
Developmentally, 'Cruising' the furniture at this stage, but not
walking independantly is within normal ranges. She may not decide to
walk alone until she feels very confident. Don't try to rush her. Play
games while she is standing holding on, for example claping hands to
encourage her to let go for short periods.
Speech: She should be vocalising, but not necessarily be forming clear
words. Making lots of different noises is like physio for the oral
muscles,getting them ready for speech. Some infants will be saying
Mama,Dada etc.
Understanding:Wheres your hair?   Wheres your toes etc should recieve
pointing answers.
Lots of Nursery rhymes will help speech develop. She will get to know
them, and in a few months try to add in repetitive words.

Diet.
Arough guide of 20ozs(1pint) of milk in 24hrs. This to include what
you add to her food. Lots of water. If she is having lots of wet
nappis, then she is getting enough fluid.
Toddlers tend to 'graze'. They should eat little and often. You'll
find they can go a few days seemingly not eating very much,then a few
where they have a great appetite! Again try not to worry,esp if she is
growing well.