You cannot infer a tree directly with BioPerl, but you can run alignment and tree inference programs through the bioperl-run package. Since you are starting out, I recommend not going that route because that adds another layer of technical difficulty if you are not familiar with Perl/BioPerl. The basic steps are:

1. Create a FASTA file of your proteins.
2. Align these sequence using a multiple sequence alignment program like MUSCLE.
3. Generate a tree using one of four main paradigms for tree inference (Parsimony, ML, NJ, or Bayesian methods).
4. Convert the tree to Newick (if necessary) for plotting with BioPerl.

All of these steps can be done online, especially for 10 sequences. When you get to step four have a look at the BioPerl HOWTO page for saving images of trees. Also, consider using the separate Bio::Phylo package for phylogenomics work with Perl.