please help: Is this R-syntax is true?

#1
I want to ask some confusing in my mind regarding the data analysis:

I have conducting the experimental trial in repeated measure by hours as below:

Design: Completely Randomized Design--(in green houses)-there are 6 box unit
========================================================
- 1 Treatment (2 levels): level A and B
- Replicate: 3 replication
- Response was recorded by hours (repeated measure) from 24 hours (poisson distribution)

This follows as linear mixed model.

and I used $R$ to process my data by using this syntax:
Code:
>Random intercepts for 3 rep but time and treat effects are fixed 
>model1 <-lmer(respon~ treat * time + rep + (1|rep), data=data, family = poisson)
OUTPUT is:

>
Code:
model1
      Generalized linear mixed model fit by the Laplace approximation 
      Formula: respon ~ treat * time + rep + (1 | rep) 
      Data: data 
      AIC BIC logLik deviance
      720 740   -354      708
      Random effects:
      Groups Name        Variance  Std.Dev.
      rep    (Intercept) 0.0078266 0.088468
      Number of obs: 207, groups: rep, 3

      Fixed effects           
      Estimate Std. Error z value Pr(>|z|)   
      (Intercept)  0.843199   0.311791  2.7044  0.00684 **
      treat       -0.246484   0.124762 -1.9756  0.04820 * 
      time         0.010138   0.016759  0.6049  0.54523   
      rep          0.063730   0.082557  0.7719  0.44015   
      treat:time   0.009520   0.008028  1.1858  0.23569   
      ---
      Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

**MY QUESTION IS: is my syntax above TRUE?**


Thanks in advanced